Question

1)

A random sample of 64 second- graders in a certain school district are given a standardized mathematics skills test. The sample mean score is 51.60. Assume the standard deviation for the population of test scores is 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average. Perform the hypothesis test and compute the p -value.

Write down your p -value. You will need it for the next question.

Round your answer to four decimal places (for example: 0.2305). Write only a number as your answer.

2)

Recall the previous question where the school superintendent wanted to know whether second-graders in her school district have greater math skills than the nationwide average. Based on your P-value, what is the conclusion if we test at the 0.05 level of significance?

A) This is not enough evidence to conclude that the second-graders in her district have greater math skills.

B) There is evidence to conclude that the second-graders in her district do not have greater math skills.

C) There is not enough evidence to conclude that the second-graders in her district do not have greater math skills.

D) There is evidence to conclude that the second-graders in her district have greater math skills.

Answer 1

We use Z-test for signifcance of population mean to test that the second graders in her school district have greater math skills than the nation-wide average.

Hypothesis -

Null hypothesis - H₀ : nation-wide average score is equal to 50. i.e. = 50.

Alternative hypothesis - H₁ : school district have greater math skills than the nation-wide average. . i.e. > 50.

Test statistic -

Test criterion -

We reject H₀ if p-value is less than 0.05.

Calculations -

A random sample of 64 second-graders be chosen so that their mean score is 51.60 marks. The population standard deviation is 15.

So, = 500, = 51.6, n=64, = 15

p-value = P(Z>z) = P(Z>0.8533) = 1-P(Z<0.8533) = 0.1967

Conclusion -

p-value > 0.05, we do not reject H₀ at 5% level of significance.

Result -

This is not enough evidence that the second grader in her district have greater math skills.

Option A is correct.