Describe what it means for a method of constructing confidence intervals to prod

Question

Describe what it means for a method of constructing confidence intervals to produce "valid' intervals List the assumptions necessary for an equal-variance two-sample t-test comparing two population means to be valid. SHORT You randomly select 20 dorm rooms that each house one Biology major and one Psychology major. You ask each student what their typical bedtime is, and you plan to use this sample to test the null hypothesis that students from these majors have the same average bedtime. What test should you use?

Explanation / Answer

1. This means that the nominal coverage probability (confidence level) of the confidence interval should hold, either exactly or to a good approximation.

Assumptions for Validity of Confidence Interval and Hypothesis test for :

2. Assumptions for equal variance two sample t-tests :

When running a two-sample equal-variance t-test, the basic assumptions are that the distributions of the two populations are normal, and that the variances of the two distributions are the same. If those assumptions are not likely to be met, another testing procedure could be used, and the corresponding procedure in PASS should be used for sample size or power calculations.

3. Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not=mu2

where mu1 is the population mean for Biology major and

mu2 is the population mean for Psychology major.

Here sample size is 20 which is less than 30 therefore we use two sample t-test.

Here condition on variance is not given therefore we use equal variances.

So finally we use two sample t-test assuming equal variances.

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