*Sample Size Matters Uncertainty in Measurement вЂ“ Tom Hopper Calculation of effect size estimates from information that is reported When a researcher has access to a full set of summary data such as the mean, standard deviation, and sample size for each group, the computation of the effect size and its variance is relatively straightforward. In practice, however, the*

How to find standard deviation with ONLY sample size?. Hence, the standard deviation of that $N$-count sample, treated as a population, will systematically underestimate the standard deviation of the population. For example, with $N = 3$, if you draw $12, 14, 16$, you have an average of $14$., 19/12/2014В В· To estimate the sample mean and standard deviation, we first review the Hozo et al.вЂ™s method and point out some limitations of their method in estimating the sample standard deviation. We then propose to improve their estimation by incorporating the information of the sample size..

Note that all this only works if you know the population standard deviation. If you're computing an estimate of the expected range from the sample standard deviation you need to know about the behavior of the ratio of sample range to sample standard deviation. [1]: L. H. C. Tippett (1925). "On the Extreme Individuals and the Range of Samples 12/08/2018В В· In high school, I was taught that the standard deviation drops as you increase the sample size. For this reason, larger sample sizes produce less fluctuation. At the time, I didn't question this because it made sense. Then, I was taught that the standard deviation does not drop as you increase

Standard deviation and sample size. Likewise, when we calculate the sample standard deviation, , the true standard deviation, has a 95% chance of being within the confidence band below. For small sample sizes (roughly less than 10), the measured standard deviation can be off from the true standard deviation by several times. Note that all this only works if you know the population standard deviation. If you're computing an estimate of the expected range from the sample standard deviation you need to know about the behavior of the ratio of sample range to sample standard deviation. [1]: L. H. C. Tippett (1925). "On the Extreme Individuals and the Range of Samples

Note that all this only works if you know the population standard deviation. If you're computing an estimate of the expected range from the sample standard deviation you need to know about the behavior of the ratio of sample range to sample standard deviation. [1]: L. H. C. Tippett (1925). "On the Extreme Individuals and the Range of Samples Standard deviation and sample size. Likewise, when we calculate the sample standard deviation, , the true standard deviation, has a 95% chance of being within the confidence band below. For small sample sizes (roughly less than 10), the measured standard deviation can be off from the true standard deviation by several times.

Users may supply the values for the below input parameters to find the effective sample size to be statistically significant by using this sample size calculator. Confidence level : It's a measure of probability that the confidence interval have the unknown parameter of population, generally represented by 1 - О±. 0.01, 0.05, 0.10 & 0.5 represents 99%, 95%, 90% and 50% confidence levels respectively. Two samples were taken from the population. One sample had 25 subjects and the standard deviation 4.5 on some key variable. The other sample had 12 subjects and had a standard deviation of 6.4 on the same key variable. Is there a significant difference between the variances of the two samples? First standard deviation: 4.5. First sample size: 25

The next stage distinguishes between the sample standard deviation and the population standard deviation. For the sample deviation, you divide this result by the sample size minus one (n в€’1). In our example, n = 10, so n вЂ“ 1 = 9. 19/12/2014В В· To estimate the sample mean and standard deviation, we first review the Hozo et al.вЂ™s method and point out some limitations of their method in estimating the sample standard deviation. We then propose to improve their estimation by incorporating the information of the sample size.

19/12/2014В В· To estimate the sample mean and standard deviation, we first review the Hozo et al.вЂ™s method and point out some limitations of their method in estimating the sample standard deviation. We then propose to improve their estimation by incorporating the information of the sample size. Standard deviation and sample size. Likewise, when we calculate the sample standard deviation, , the true standard deviation, has a 95% chance of being within the confidence band below. For small sample sizes (roughly less than 10), the measured standard deviation can be off from the true standard deviation by several times.

Use of the sample standard deviation implies that these 14 fulmars are a sample from a larger population of fulmars. If these 14 fulmars comprised the entire population (perhaps the last 14 surviving fulmars), then instead of the sample standard deviation, the calculation would use the population standard deviation. Standard deviation and sample size. Likewise, when we calculate the sample standard deviation, , the true standard deviation, has a 95% chance of being within the confidence band below. For small sample sizes (roughly less than 10), the measured standard deviation can be off from the true standard deviation by several times.

Confidence Intervals for One Standard Deviation using Standard Deviation procedure window by expanding Variances, then clicking on One Standard Deviation, and then clicking on Confidence Intervals for One Standard Deviation using Standard Deviation. You may then make the appropriate entries as listed below, or open Example 2 by going to the File 12/08/2018В В· In high school, I was taught that the standard deviation drops as you increase the sample size. For this reason, larger sample sizes produce less fluctuation. At the time, I didn't question this because it made sense. Then, I was taught that the standard deviation does not drop as you increase

Two samples were taken from the population. One sample had 25 subjects and the standard deviation 4.5 on some key variable. The other sample had 12 subjects and had a standard deviation of 6.4 on the same key variable. Is there a significant difference between the variances of the two samples? First standard deviation: 4.5. First sample size: 25 Users may supply the values for the below input parameters to find the effective sample size to be statistically significant by using this sample size calculator. Confidence level : It's a measure of probability that the confidence interval have the unknown parameter of population, generally represented by 1 - О±. 0.01, 0.05, 0.10 & 0.5 represents 99%, 95%, 90% and 50% confidence levels respectively.

Standard deviation and sample size. Likewise, when we calculate the sample standard deviation, , the true standard deviation, has a 95% chance of being within the confidence band below. For small sample sizes (roughly less than 10), the measured standard deviation can be off from the true standard deviation by several times. Users may supply the values for the below input parameters to find the effective sample size to be statistically significant by using this sample size calculator. Confidence level : It's a measure of probability that the confidence interval have the unknown parameter of population, generally represented by 1 - О±. 0.01, 0.05, 0.10 & 0.5 represents 99%, 95%, 90% and 50% confidence levels respectively.

Two-Sample T-Test from Means and SDвЂ™s Sample Size Software. Hence, the standard deviation of that $N$-count sample, treated as a population, will systematically underestimate the standard deviation of the population. For example, with $N = 3$, if you draw $12, 14, 16$, you have an average of $14$., Confidence Intervals for One Standard Deviation using Standard Deviation procedure window by expanding Variances, then clicking on One Standard Deviation, and then clicking on Confidence Intervals for One Standard Deviation using Standard Deviation. You may then make the appropriate entries as listed below, or open Example 2 by going to the File.

Comparing Histograms dummies. Calculation of effect size estimates from information that is reported When a researcher has access to a full set of summary data such as the mean, standard deviation, and sample size for each group, the computation of the effect size and its variance is relatively straightforward. In practice, however, the https://en.wikipedia.org/wiki/Standard_error_of_the_mean If the population from which the samples are drawn is normally distributed with mean Ој and standard deviation Пѓ, then the sampling distribution of the sample mean, xВЇ, will also be normally distributed with the following mean and standard deviation, regardless of the sample size: ОјxВЇ=Ој and ПѓxВЇ=Пѓ/n^(1/2).

Users may supply the values for the below input parameters to find the effective sample size to be statistically significant by using this sample size calculator. Confidence level : It's a measure of probability that the confidence interval have the unknown parameter of population, generally represented by 1 - О±. 0.01, 0.05, 0.10 & 0.5 represents 99%, 95%, 90% and 50% confidence levels respectively. Find the standard deviation of the sample proportion for a sample of size 150, when we assume equal probabilities for the wins and losses of a football tournament. Assume also, that the number of outcomes in the population ( N) is very large, essentially infinite.

Confidence Intervals for One Standard Deviation using Standard Deviation procedure window by expanding Variances, then clicking on One Standard Deviation, and then clicking on Confidence Intervals for One Standard Deviation using Standard Deviation. You may then make the appropriate entries as listed below, or open Example 2 by going to the File If the population from which the samples are drawn is normally distributed with mean Ој and standard deviation Пѓ, then the sampling distribution of the sample mean, xВЇ, will also be normally distributed with the following mean and standard deviation, regardless of the sample size: ОјxВЇ=Ој and ПѓxВЇ=Пѓ/n^(1/2)

Confidence Intervals for One Standard Deviation using Standard Deviation procedure window by expanding Variances, then clicking on One Standard Deviation, and then clicking on Confidence Intervals for One Standard Deviation using Standard Deviation. You may then make the appropriate entries as listed below, or open Example 2 by going to the File Standard deviation and sample size. Likewise, when we calculate the sample standard deviation, , the true standard deviation, has a 95% chance of being within the confidence band below. For small sample sizes (roughly less than 10), the measured standard deviation can be off from the true standard deviation by several times.

Use of the sample standard deviation implies that these 14 fulmars are a sample from a larger population of fulmars. If these 14 fulmars comprised the entire population (perhaps the last 14 surviving fulmars), then instead of the sample standard deviation, the calculation would use the population standard deviation. Two samples were taken from the population. One sample had 25 subjects and the standard deviation 4.5 on some key variable. The other sample had 12 subjects and had a standard deviation of 6.4 on the same key variable. Is there a significant difference between the variances of the two samples? First standard deviation: 4.5. First sample size: 25

Users may supply the values for the below input parameters to find the effective sample size to be statistically significant by using this sample size calculator. Confidence level : It's a measure of probability that the confidence interval have the unknown parameter of population, generally represented by 1 - О±. 0.01, 0.05, 0.10 & 0.5 represents 99%, 95%, 90% and 50% confidence levels respectively. Find the standard deviation of the sample proportion for a sample of size 150, when we assume equal probabilities for the wins and losses of a football tournament. Assume also, that the number of outcomes in the population ( N) is very large, essentially infinite.

Find the standard deviation of the sample proportion for a sample of size 150, when we assume equal probabilities for the wins and losses of a football tournament. Assume also, that the number of outcomes in the population ( N) is very large, essentially infinite. Find the standard deviation of the sample proportion for a sample of size 150, when we assume equal probabilities for the wins and losses of a football tournament. Assume also, that the number of outcomes in the population ( N) is very large, essentially infinite.

Calculation of effect size estimates from information that is reported When a researcher has access to a full set of summary data such as the mean, standard deviation, and sample size for each group, the computation of the effect size and its variance is relatively straightforward. In practice, however, the 19/12/2014В В· To estimate the sample mean and standard deviation, we first review the Hozo et al.вЂ™s method and point out some limitations of their method in estimating the sample standard deviation. We then propose to improve their estimation by incorporating the information of the sample size.

Means and Full Sample Standard Deviation; Means Gains Scores and Gain Score Standard Deviations; Means Gains Scores, Pre and Post SDs, and Paired T-Tests; Means Gains Scores, Pre and Post SDs, and Pre-Post r; Means and Standard Deviations with Sub-groups; F-Test, 3 or More Groups; Means and ANCOVA; Two-way ANOVA, Means, and Sample Sizes Note that all this only works if you know the population standard deviation. If you're computing an estimate of the expected range from the sample standard deviation you need to know about the behavior of the ratio of sample range to sample standard deviation. [1]: L. H. C. Tippett (1925). "On the Extreme Individuals and the Range of Samples

Note that all this only works if you know the population standard deviation. If you're computing an estimate of the expected range from the sample standard deviation you need to know about the behavior of the ratio of sample range to sample standard deviation. [1]: L. H. C. Tippett (1925). "On the Extreme Individuals and the Range of Samples Sample Mean +/- (z * standard deviation) / N.5 Sample Mean +/- $1000 Introductory statistics textbooks provide the following formula for determining the sample size required to meet a desired ME, N = (z2 * s2) / e2 N = (1.645 * 1.645) * (7,500 * 7,500) / (1,000 * 1,000) N = 152.21 where e is the ME, s is the estimated standard deviation, z is the value associated with his desired level of

Confidence Intervals for One Standard Deviation using Standard Deviation procedure window by expanding Variances, then clicking on One Standard Deviation, and then clicking on Confidence Intervals for One Standard Deviation using Standard Deviation. You may then make the appropriate entries as listed below, or open Example 2 by going to the File Hence, the standard deviation of that $N$-count sample, treated as a population, will systematically underestimate the standard deviation of the population. For example, with $N = 3$, if you draw $12, 14, 16$, you have an average of $14$.

This number is not known, so you do a pilot study of 35 students and find the standard deviation (s) for the sample is 148 songs вЂ” use this number as a substitute for Using the sample size formula, you calculate the sample size you need is Because the sample size is 100, the median will be between the 50th and 51st data value when the data is sorted from lowest to highest. To find the bar that contains the median, count the heights of the bars until you reach 50 and 51. The bar containing the median has the range 78.75 to 80.

Two-Sample T-Test from Means and SDвЂ™s Sample Size Software. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution?, As sample size increases (for example, a trading strategy with an 80% edge), why does the standard deviation of results get smaller? Can someone please explain why standard deviation gets smaller and.

Means and Standard Deviations Center for Evidence-Based. This number is not known, so you do a pilot study of 35 students and find the standard deviation (s) for the sample is 148 songs вЂ” use this number as a substitute for Using the sample size formula, you calculate the sample size you need is, Find the standard deviation of the sample proportion for a sample of size 150, when we assume equal probabilities for the wins and losses of a football tournament. Assume also, that the number of outcomes in the population ( N) is very large, essentially infinite..

Because the sample size is 100, the median will be between the 50th and 51st data value when the data is sorted from lowest to highest. To find the bar that contains the median, count the heights of the bars until you reach 50 and 51. The bar containing the median has the range 78.75 to 80. Find the standard deviation of the sample proportion for a sample of size 150, when we assume equal probabilities for the wins and losses of a football tournament. Assume also, that the number of outcomes in the population ( N) is very large, essentially infinite.

Users may supply the values for the below input parameters to find the effective sample size to be statistically significant by using this sample size calculator. Confidence level : It's a measure of probability that the confidence interval have the unknown parameter of population, generally represented by 1 - О±. 0.01, 0.05, 0.10 & 0.5 represents 99%, 95%, 90% and 50% confidence levels respectively. estimation problem and proposed a simple method for estimating the sample mean and the sample variance (or equivalently the sample standard deviation) from the median, range, and the size of the sample. Their method is now widely accepted in the literature of systematic reviews and meta-analysis. For instance, a search of Google Scholar on 18

Because the sample size is 100, the median will be between the 50th and 51st data value when the data is sorted from lowest to highest. To find the bar that contains the median, count the heights of the bars until you reach 50 and 51. The bar containing the median has the range 78.75 to 80. Two samples were taken from the population. One sample had 25 subjects and the standard deviation 4.5 on some key variable. The other sample had 12 subjects and had a standard deviation of 6.4 on the same key variable. Is there a significant difference between the variances of the two samples? First standard deviation: 4.5. First sample size: 25

Sample Mean +/- (z * standard deviation) / N.5 Sample Mean +/- $1000 Introductory statistics textbooks provide the following formula for determining the sample size required to meet a desired ME, N = (z2 * s2) / e2 N = (1.645 * 1.645) * (7,500 * 7,500) / (1,000 * 1,000) N = 152.21 where e is the ME, s is the estimated standard deviation, z is the value associated with his desired level of Note that all this only works if you know the population standard deviation. If you're computing an estimate of the expected range from the sample standard deviation you need to know about the behavior of the ratio of sample range to sample standard deviation. [1]: L. H. C. Tippett (1925). "On the Extreme Individuals and the Range of Samples

As sample size increases (for example, a trading strategy with an 80% edge), why does the standard deviation of results get smaller? Can someone please explain why standard deviation gets smaller and Find the standard deviation of the sample proportion for a sample of size 150, when we assume equal probabilities for the wins and losses of a football tournament. Assume also, that the number of outcomes in the population ( N) is very large, essentially infinite.

Calculation of effect size estimates from information that is reported When a researcher has access to a full set of summary data such as the mean, standard deviation, and sample size for each group, the computation of the effect size and its variance is relatively straightforward. In practice, however, the 12/08/2018В В· In high school, I was taught that the standard deviation drops as you increase the sample size. For this reason, larger sample sizes produce less fluctuation. At the time, I didn't question this because it made sense. Then, I was taught that the standard deviation does not drop as you increase

Use of the sample standard deviation implies that these 14 fulmars are a sample from a larger population of fulmars. If these 14 fulmars comprised the entire population (perhaps the last 14 surviving fulmars), then instead of the sample standard deviation, the calculation would use the population standard deviation. Confidence Intervals for One Standard Deviation using Standard Deviation procedure window by expanding Variances, then clicking on One Standard Deviation, and then clicking on Confidence Intervals for One Standard Deviation using Standard Deviation. You may then make the appropriate entries as listed below, or open Example 2 by going to the File

If the population from which the samples are drawn is normally distributed with mean Ој and standard deviation Пѓ, then the sampling distribution of the sample mean, xВЇ, will also be normally distributed with the following mean and standard deviation, regardless of the sample size: ОјxВЇ=Ој and ПѓxВЇ=Пѓ/n^(1/2) estimation problem and proposed a simple method for estimating the sample mean and the sample variance (or equivalently the sample standard deviation) from the median, range, and the size of the sample. Their method is now widely accepted in the literature of systematic reviews and meta-analysis. For instance, a search of Google Scholar on 18

12/08/2018В В· In high school, I was taught that the standard deviation drops as you increase the sample size. For this reason, larger sample sizes produce less fluctuation. At the time, I didn't question this because it made sense. Then, I was taught that the standard deviation does not drop as you increase The next stage distinguishes between the sample standard deviation and the population standard deviation. For the sample deviation, you divide this result by the sample size minus one (n в€’1). In our example, n = 10, so n вЂ“ 1 = 9.

Means and Standard Deviations Center for Evidence-Based. Sample Mean +/- (z * standard deviation) / N.5 Sample Mean +/- $1000 Introductory statistics textbooks provide the following formula for determining the sample size required to meet a desired ME, N = (z2 * s2) / e2 N = (1.645 * 1.645) * (7,500 * 7,500) / (1,000 * 1,000) N = 152.21 where e is the ME, s is the estimated standard deviation, z is the value associated with his desired level of, As sample size increases (for example, a trading strategy with an 80% edge), why does the standard deviation of results get smaller? Can someone please explain why standard deviation gets smaller and.

Comparing Histograms dummies. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution?, Find the standard deviation of the sample proportion for a sample of size 150, when we assume equal probabilities for the wins and losses of a football tournament. Assume also, that the number of outcomes in the population ( N) is very large, essentially infinite..

Sample size 400 sample mean 44 sample standard deviation. Use of the sample standard deviation implies that these 14 fulmars are a sample from a larger population of fulmars. If these 14 fulmars comprised the entire population (perhaps the last 14 surviving fulmars), then instead of the sample standard deviation, the calculation would use the population standard deviation. https://en.wikipedia.org/wiki/Standard_error_of_the_mean Users may supply the values for the below input parameters to find the effective sample size to be statistically significant by using this sample size calculator. Confidence level : It's a measure of probability that the confidence interval have the unknown parameter of population, generally represented by 1 - О±. 0.01, 0.05, 0.10 & 0.5 represents 99%, 95%, 90% and 50% confidence levels respectively..

estimation problem and proposed a simple method for estimating the sample mean and the sample variance (or equivalently the sample standard deviation) from the median, range, and the size of the sample. Their method is now widely accepted in the literature of systematic reviews and meta-analysis. For instance, a search of Google Scholar on 18 Hence, the standard deviation of that $N$-count sample, treated as a population, will systematically underestimate the standard deviation of the population. For example, with $N = 3$, if you draw $12, 14, 16$, you have an average of $14$.

Because the sample size is 100, the median will be between the 50th and 51st data value when the data is sorted from lowest to highest. To find the bar that contains the median, count the heights of the bars until you reach 50 and 51. The bar containing the median has the range 78.75 to 80. The next stage distinguishes between the sample standard deviation and the population standard deviation. For the sample deviation, you divide this result by the sample size minus one (n в€’1). In our example, n = 10, so n вЂ“ 1 = 9.

Because the sample size is 100, the median will be between the 50th and 51st data value when the data is sorted from lowest to highest. To find the bar that contains the median, count the heights of the bars until you reach 50 and 51. The bar containing the median has the range 78.75 to 80. If the population from which the samples are drawn is normally distributed with mean Ој and standard deviation Пѓ, then the sampling distribution of the sample mean, xВЇ, will also be normally distributed with the following mean and standard deviation, regardless of the sample size: ОјxВЇ=Ој and ПѓxВЇ=Пѓ/n^(1/2)

19/12/2014В В· In meta-analysis of continuous outcomes, the sample size, mean, and standard deviation are required from included studies. This, however, can be difficult because results from different studies are often presented in different and non-consistent forms. Specifically in medical research, instead of reporting the sample mean and standard deviation Hence, the standard deviation of that $N$-count sample, treated as a population, will systematically underestimate the standard deviation of the population. For example, with $N = 3$, if you draw $12, 14, 16$, you have an average of $14$.

If the population from which the samples are drawn is normally distributed with mean Ој and standard deviation Пѓ, then the sampling distribution of the sample mean, xВЇ, will also be normally distributed with the following mean and standard deviation, regardless of the sample size: ОјxВЇ=Ој and ПѓxВЇ=Пѓ/n^(1/2) Means and Full Sample Standard Deviation; Means Gains Scores and Gain Score Standard Deviations; Means Gains Scores, Pre and Post SDs, and Paired T-Tests; Means Gains Scores, Pre and Post SDs, and Pre-Post r; Means and Standard Deviations with Sub-groups; F-Test, 3 or More Groups; Means and ANCOVA; Two-way ANOVA, Means, and Sample Sizes

Users may supply the values for the below input parameters to find the effective sample size to be statistically significant by using this sample size calculator. Confidence level : It's a measure of probability that the confidence interval have the unknown parameter of population, generally represented by 1 - О±. 0.01, 0.05, 0.10 & 0.5 represents 99%, 95%, 90% and 50% confidence levels respectively. Standard deviation and sample size. Likewise, when we calculate the sample standard deviation, , the true standard deviation, has a 95% chance of being within the confidence band below. For small sample sizes (roughly less than 10), the measured standard deviation can be off from the true standard deviation by several times.

If the population from which the samples are drawn is normally distributed with mean Ој and standard deviation Пѓ, then the sampling distribution of the sample mean, xВЇ, will also be normally distributed with the following mean and standard deviation, regardless of the sample size: ОјxВЇ=Ој and ПѓxВЇ=Пѓ/n^(1/2) This number is not known, so you do a pilot study of 35 students and find the standard deviation (s) for the sample is 148 songs вЂ” use this number as a substitute for Using the sample size formula, you calculate the sample size you need is

Standard deviation and sample size. Likewise, when we calculate the sample standard deviation, , the true standard deviation, has a 95% chance of being within the confidence band below. For small sample sizes (roughly less than 10), the measured standard deviation can be off from the true standard deviation by several times. 19/12/2014В В· In meta-analysis of continuous outcomes, the sample size, mean, and standard deviation are required from included studies. This, however, can be difficult because results from different studies are often presented in different and non-consistent forms. Specifically in medical research, instead of reporting the sample mean and standard deviation

The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution? Means and Full Sample Standard Deviation; Means Gains Scores and Gain Score Standard Deviations; Means Gains Scores, Pre and Post SDs, and Paired T-Tests; Means Gains Scores, Pre and Post SDs, and Pre-Post r; Means and Standard Deviations with Sub-groups; F-Test, 3 or More Groups; Means and ANCOVA; Two-way ANOVA, Means, and Sample Sizes

Because the sample size is 100, the median will be between the 50th and 51st data value when the data is sorted from lowest to highest. To find the bar that contains the median, count the heights of the bars until you reach 50 and 51. The bar containing the median has the range 78.75 to 80. Note that all this only works if you know the population standard deviation. If you're computing an estimate of the expected range from the sample standard deviation you need to know about the behavior of the ratio of sample range to sample standard deviation. [1]: L. H. C. Tippett (1925). "On the Extreme Individuals and the Range of Samples

The next stage distinguishes between the sample standard deviation and the population standard deviation. For the sample deviation, you divide this result by the sample size minus one (n в€’1). In our example, n = 10, so n вЂ“ 1 = 9. Two samples were taken from the population. One sample had 25 subjects and the standard deviation 4.5 on some key variable. The other sample had 12 subjects and had a standard deviation of 6.4 on the same key variable. Is there a significant difference between the variances of the two samples? First standard deviation: 4.5. First sample size: 25