Which of the following tests should be used to evaluate the difference between the means of two normally distributed populations?An approximate t-test if the population variances are unknown and assumed unequal and the samples are assumed to be independent.An approximate t-test that involves the calculation of a pooled estimator of the population variances which are assumed unequal.A paired comparison test if the two samples are independent and the population variances are unknown
Question
Which of the following tests should be used to evaluate the difference between the means of two normally distributed populations?An approximate t-test if the population variances are unknown and assumed unequal and the samples are assumed to be independent.An approximate t-test that involves the calculation of a pooled estimator of the population variances which are assumed unequal.A paired comparison test if the two samples are independent and the population variances are unknown
Solution
The appropriate test to evaluate the difference between the means of two normally distributed populations depends on the assumptions about the population variances and the independence of the samples.
-
An approximate t-test if the population variances are unknown and assumed unequal and the samples are assumed to be independent: This is known as the Welch's t-test. It is used when the two samples are independent, and the variances of the two populations are not assumed to be equal.
-
An approximate t-test that involves the calculation of a pooled estimator of the population variances which are assumed unequal: This seems to be a misinterpretation. The pooled variance t-test, also known as the Student's t-test, assumes that the population variances are equal, not unequal.
-
A paired comparison test if the two samples are independent and the population variances are unknown: This is not correct. A paired t-test is used when the samples are dependent, not independent.
So, based on the given conditions, the first option, the Welch's t-test, would be the most appropriate test to use.
Similar Questions
The t test for the difference between the means of two independent populationsalways assumes that the respectivea. sample sizes are equalb. sample variances are equalc. populations are normally distributed if each sample size is less than 30d. All of the above
Which one of the following statements are true about a 2-Sample t-test? It is used to compare differences between two group medians The variances of the two samples are statistically different. The samples to be compared must include the same number of observations Both samples must be from normally distributed processes
Which of the following statements is true for calculating the t-score for an independent two-sample t-test?A: We use the sample means, sample sizes, and a pooled standard deviation.B: We use the sample means, sample sizes, and the population standard deviation.C: We use the mean difference between the samples, the standard deviation of the samples, and the average sample size.D: We use the mean difference between the samples, the standard deviation of the differences, and the sample size.
Which statistical test is commonly used to compare the means of two independent samples?a.t-testb.Analysis of Variance (ANOVA)c.Chi-square testd.Paired t-testClear my choice
In a two-sample t-test, there are two approaches: considering the equal variance and considering the unequal variance. What test is used to check if the variance of the two populations is equal or not?a.F testb.t testc.Z testd.Chi-square test
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.