When samples are dependent, regardless of the sample size we have to use the t-student test...

When samples are dependent, regardless of the sample size we have to use the t-student test statistic with d.f. = n - 1. Suppose we want to compare the premium prices of Progressive Insurance and State Farm Insurance. We want to find out which one is cheaper. Let's suppose we ask 20 people to call Progressive and State Farm to figure out their premiums for the same coverage. The same 20 people call Progressive and State Farm. So, their 20 pairs of premiums would constitute paired data, and the two samples would be dependent samples. The critical value for the test is

df = n-1 = 20-1 = 19

What would be the critical value for the test if we have a right-tailed test with a significance level of 0.05?

Expert Solution

Solution,

Given that,

n = 20

degrees of freedom = n - 1 = 20 - 1 = 19

= 0.05

This is right tailed test,

P( T > t ) = 0.05

= 1 - P( T < t) = 0.05

= P(T < t ) = 1 - 0.05

= P(T < t ) = 0.95

= P(T < 1.729 ) = 0.95

critical value = 1.729

orchestra answered 2 years ago

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