We want to compare two different variances from a normally distributed sample that are independent of...
We want to compare two different variances from a normally distributed sample that are independent of each other. What test should we use?
Chi square, Linear regression, F-ratio, or Two-way ANOVA?
Homework Answers
F-ratio
An F-test is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal
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We want to compare two different variances from
a normally distributed sample that are independent
of...
The difference of two independent normally distributed random variables is also normally distributed. We have used...
The difference of two independent normally distributed random
variables is also normally distributed. We have used this fact in
many of our derivations. Now, consider two independent and normally
distributed populations with unknown variances σ 2 X and σ 2 Y . If
we get a random sample X1, X2, . . . , Xn from the first population
and a random sample Y1, Y2, . . . , Yn from the second population
(note that both samples are of...
QUESTION 7 The following data are taken from three different populations known to be normally distributed,...
QUESTION 7 The following data are taken from three different populations known to be normally distributed, with equal population variances based on independent simple random samples. Sample 1 Sample 2 Sample 3 39 40 43 37 38 50 35 33 42 45 35 54 37 30 48 30 52 Given that one-way ANOVA was performed and we reject the null hypothesis, please use Tuley's test to determine which pairwise means differ using a familywise error rate of a -0.05. 22...
The following data represent the results from an independent-measures study comparing two treatment conditions. Treatment Treatment...
The following data represent the results from an independent-measures study comparing two treatment conditions. Treatment Treatment One Two 2.5 7.2 5.2 7.6 5.8 4.4 6.3 4.5 4.7 5.2 4.8 3 Using technology, run the One-way ANOVA Test for this data: F-ratio: p-value: Now, run the Two Independent Sample t test on the same data: Note: Do this with "pooled variances" since one assumption we make with ANOVA is that the variances for each group are equal. t-statistic: p-value: Do you...
Consider the following measures based on independently drawn samples from normally distributed populations: (You may find...
Consider the following measures based on independently drawn samples from normally distributed populations: (You may find it useful to reference the appropriate table: chi-square table or F table) Sample 1: s21s12 = 221, and n1 = 16 Sample 2: s22s22 = 208, and n2 = 11 a. Construct the 95% interval estimate for the ratio of the population variances. (Round "F" value and final answers to 2 decimal places.) Confidence interval _______ to _______ B. Using the confidence interval from...
Consider the following measures based on independently drawn samples from normally distributed populations Ợou may find...
Consider the following measures based on independently drawn samples from normally distributed populations Ợou may find it useful to reference the appropriate table: chi-square table or F table) Sample 1: s 221, and n1 - 16 Sample 2:s 208, and n2 11 a. Construct the 95% interval estimate for the ratio of the population variances. (Round "F' value and final answers to 2 decimal places.) Confidence interval to b. Using the confidence interval from Part (a), test if the ratio...
Assume that two samples are independent simple random samples selected from normally distributed populations, and do...
Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that mothers spend more time (in minutes) driving their kids to activities than fathers do? A. F B. t C. Chi-square D. Normal
The following information was obtained from independent random samples. Assume normally distributed populations with equal variances....
The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Size 10 12 Sample Mean 52 51 Sample Variance 85 90 We are interested in testing H0: μSample 1 - μSample 2 = 0 Ha: μSample 1 - μSample 2 ≠ 0 Step 1 of 3: What is the value of the test statistic? Round your answer to four decimal places.
Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in...
Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 26 roller bearings from the old manufacturing process showed the sample variance of diameters to be s2 = 0.231. Another random sample of 28 roller bearings from the new manufacturing process showed the sample variance of their diameters to be s2 = 0.146. Use a 5% level of significance to test the claim that there is...
Two samples each of size 20 are taken from independent populations assumed to be normally distributed...
Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and a standard deviation of 4.1 while the second sample has a mean of 40.1 and a standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude? There is not sufficient evidence to reject...
Exercise 11-26 Algo Consider the following measures based on independently drawn samples from normally distributed populations:...
Exercise 11-26 Algo Consider the following measures based on independently drawn samples from normally distributed populations: (You may find it useful to reference the appropriate table: chi-square table or F table) Sample 1: -276, and -51 Sample 2: s2 164, and n2 26 a. Construct the 90% interval estimate for the ratio of the population variances. Round "P' value and final answers to 2 decimal places.) Confidence interval to b. Using the confidence interval from Part (a), test if the...
The difference of two independent normally distributed random
variables is also normally distributed. We have used this fact in
many of our derivations. Now, consider two independent and normally
distributed populations with unknown variances σ 2 X and σ 2 Y . If
we get a random sample X1, X2, . . . , Xn from the first population
and a random sample Y1, Y2, . . . , Yn from the second population
(note that both samples are of...
QUESTION 7 The following data are taken from three different populations known to be normally distributed, with equal population variances based on independent simple random samples. Sample 1 Sample 2 Sample 3 39 40 43 37 38 50 35 33 42 45 35 54 37 30 48 30 52 Given that one-way ANOVA was performed and we reject the null hypothesis, please use Tuley's test to determine which pairwise means differ using a familywise error rate of a -0.05. 22...
The following data represent the results from an independent-measures study comparing two treatment conditions. Treatment Treatment One Two 2.5 7.2 5.2 7.6 5.8 4.4 6.3 4.5 4.7 5.2 4.8 3 Using technology, run the One-way ANOVA Test for this data: F-ratio: p-value: Now, run the Two Independent Sample t test on the same data: Note: Do this with "pooled variances" since one assumption we make with ANOVA is that the variances for each group are equal. t-statistic: p-value: Do you...
Consider the following measures based on independently drawn samples from normally distributed populations Ợou may find it useful to reference the appropriate table: chi-square table or F table) Sample 1: s 221, and n1 - 16 Sample 2:s 208, and n2 11 a. Construct the 95% interval estimate for the ratio of the population variances. (Round "F' value and final answers to 2 decimal places.) Confidence interval to b. Using the confidence interval from Part (a), test if the ratio...
Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and a standard deviation of 4.1 while the second sample has a mean of 40.1 and a standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude? There is not sufficient evidence to reject...
Exercise 11-26 Algo Consider the following measures based on independently drawn samples from normally distributed populations: (You may find it useful to reference the appropriate table: chi-square table or F table) Sample 1: -276, and -51 Sample 2: s2 164, and n2 26 a. Construct the 90% interval estimate for the ratio of the population variances. Round "P' value and final answers to 2 decimal places.) Confidence interval to b. Using the confidence interval from Part (a), test if the...
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