Question

are you smarter than a second - grader? a random sample of 61 second - graders in a certain school district are given a standardized mathematics skills test. the sample mean score is (overline{x}=51). assume the standard deviation of test scores is (sigma = 10). the nationwide average score on this test is 54. the school superintendent wants to know whether the second - graders in her school district have different math skills than the nationwide average. use the (alpha = 0.01) level of significance and the p - value method with excel.
part: 0 / 5
part 1 of 5
(a) state the appropriate null and alternate hypotheses.
(h_0:)
(h_1:)
this hypothesis test is a (\boldsymbol{\text{select}}) test.

Explanation:

Step1: Define Null Hypothesis

The null hypothesis \( H_0 \) is a statement of no difference or equality. Here, the nationwide average score is 54, so \( H_0: \mu = 54 \).

Step2: Define Alternate Hypothesis

The superintendent wants to test if the district's scores are different from the nationwide average (two - tailed test), so \( H_1: \mu
eq 54 \). Also, since we know the population standard deviation (\( \sigma = 10 \)), this is a z - test.

Answer:

\( H_0: \boldsymbol{\mu = 54} \)
\( H_1: \boldsymbol{\mu
eq 54} \)
This hypothesis test is a \(\boldsymbol{z}\) test.