You want to explore the relationship between the grades students receive on their first two exams.For a sample of 15 students,you find a correlation coefficient of 0.47.What is the value of the test statistic for testing H₀ : p = 0 vs.H₁ : p 0? A)2.80 B)1.06 C)1.39 D)1.92

Question

You want to explore the relationship between the grades students receive on their first two exams.For a sample of 15 students,you find a correlation coefficient of 0.47.What is the value of the test statistic for testing H₀ : p = 0 vs.H₁ : p > 0? A)2.80 B)1.06 C)1.39 D)1.92

Quizplus · Accepted Answer

To determine the test statistic for this hypothesis test, we need to calculate the t-value using the formula:

t = r * sqrt(n-2) / sqrt(1-r^2)

where r is the sample correlation coefficient and n is the sample size.

Plugging in the values we have:

t = 0.47 * sqrt(15-2) / sqrt(1-0.47^2) = 1.92

Since we are testing a one-sided alternative hypothesis (p > 0), we need to find the p-value for this t-value using a t-distribution with n-2 degrees of freedom.

Using a t-table or calculator, we can find that the p-value is about 0.038.

Comparing this p-value to our chosen significance level (not given), we would either reject or fail to reject the null hypothesis.

Thus, the test statistic for this hypothesis test is 1.92, which is choice D.

You Want to Explore the Relationship Between the Grades Students