Question

Are you smarter than a second-grader? A random sample of 60 second-graders in a certain school district was given a standardized mathematics skills test. The sample mean score is x=52 Assume the standard deviation test scores is 15. The nationwide average score on this test is 50.

A. State the appropriate null and alternate hypothesis

B. Compute the value of the test statistic

C. State a conclusion. Use the 0.01 level of significance

Please show work and do NOT use MINITLAB if possible

Answer 1

Here, we have to use one sample z test for the population mean.

A. State the appropriate null and alternate hypothesis

The null and alternative hypotheses are given as below:

Null hypothesis: H0: The average score of the second grader for a standardized mathematics skills test is 50.

Alternative hypothesis: Ha: The average score of the second grader for a standardized mathematics skills test is more than 50.

H0: µ = 50 versus Ha: µ > 50

This is an upper tailed test.

B. Compute the value of the test statistic

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 50

Xbar = 52

σ = 15

n = 60

α = 0.05

Critical value = 1.6449

(by using z-table or excel)

Z = (52 - 50)/[15/sqrt(60)]

Z = 1.0328

P-value = 0.1508

(by using Z-table)

C. State a conclusion.

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the average score of the second grader for a standardized mathematics skills test is more than 50.