Question

Test C is a standardized test that all high school seniors take. In an SRS of 28 seniors, the sample standard deviation is 16. A high school counselor hypothesizes that the mean score on Test C for all high school seniors is 59.

Here are the null and alternative hypotheses: H0 : µ = 59 H1 : µ not equal to 59

(a) How far (in points) above/below 59 would the sample mean have to be to reject the null hypothesis at the 10% level ?

(b) How far (in points) above/below 59 would the sample mean have to be to reject the null hypothesis
at the 1% level?

Answer 1

Solution:-

a) For rejection the points should be less than 53.85 or greater than 64.15

For rejection p-value for test should be less than 0.10.

t-score for the p-value = + 1.704

x > 64.15

x < 53.85

b) For rejection the points should be less than 50.62 or greater than 67.38.

For rejection p-value for test should be less than 0.01.

t-score for the p-value = + 2.771

x > 67.38

x < 50.62