Asked by Satveer Sidhu on Jul 12, 2024
Verified
Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances (assumed to be unknown) .In order to test the difference between the population means,the test statistic is:
A) a standard normal random variable.
B) approximately standard normal random variable.
C) Student t-distributed with 58 degrees of freedom.
D) Student t-distributed with 33 degrees of freedom.
Independent Samples
Independent samples refer to sets of data collected from distinct, non-overlapping groups or populations, where the performance or measurement in one group does not influence the other.
Population Means
The average values of a particular variable for all individuals within a population.
- Determine the appropriate test statistic for hypothesis testing in different scenarios.
- Determine the degrees of freedom applicable to diverse t-tests.
Verified Answer
KG
Karolina GruszowskiJul 15, 2024
Final Answer :
C
Explanation :
When the population variances are unknown, we use the t-distribution to test the difference between population means. Since the sample sizes are different, we use the pooled variance and the degrees of freedom are (n1-1) + (n2-1) = 58. Therefore, the correct choice is C, Student t-distributed with 58 degrees of freedom.
Learning Objectives
- Determine the appropriate test statistic for hypothesis testing in different scenarios.
- Determine the degrees of freedom applicable to diverse t-tests.
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