Question

A random sample of 86 eighth grade students’ scores on a national mathematics assessment test has a mean score of 294. This test result prompts a state school administrator to declare that the mean score for the state’s eighth graders on this exam is more than 285. Assume the population standard deviation is 35. At the 3 % level of significance, is there enough evidence to support the administrator’s claim?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 285
Alternative Hypothesis, Ha: μ > 285

Rejection Region
This is right tailed test, for α = 0.03
Critical value of z is 1.881.
Hence reject H0 if z > 1.881

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (294 - 285)/(35/sqrt(86))
z = 2.38

P-value Approach
P-value = 0.0087
As P-value < 0.03, reject the null hypothesis.

yes, There is sufficient evidence to support the administrator’s claim