Question

Are you smarter than a second-grader? A random sample of 63 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x = 50. Assume the standard deviation of test scores is o=11. The nationwide average score on this test is 52. The school superintendent wants to know whether the second-graders in her school district have different math skills than the nationwide average. Use the = 0.10 level of significance and the P-value method with the table.

Answer 1

Solution:

Hypothesis are

H0 : $\mu$ = 52

Ha : $\mu$ $\neq$ 52

Test statistic z =
ī - Ml/o/vn
= [50 - 52]/[11/$\sqrt{}$63] = -1.44

Test statistic = -1.44

Now ,

Here , TWO  tailed test

p value = P(Z < -1.44) + P(Z > +1.44 = 0.0749 + 0.0749 = 0.1498

p value = 0.1645

P value is greater than $\alpha$ = 0.10

We fail to reject the null hypothesis

Conclusion:

There is no sufficient evidence to support the claim that the second grades in her school district have different math skills than the nationwide average.