Question

Nitterhouse Masonry Products, LLC, in Chambersburg, Pennsylvania, produces architectural concrete masonry products. The Dover, the largest block in a certain collection, is used primarily for residential retaining walls, and is manufactured to weigh 45 pounds. A quality control inspector for the company randomly selected 17 blocks, and determined that they have an average weight of 46.6 pounds with a sample standard deviation of 3.20 pounds. Assume that the distribution of the weights of the blocks is normal. Please use 4 decimal places for all critical values.

(0.5 pts.) a) Should a z or t distribution be used for statistical procedures regarding the mean? Please explain your answer.

b) Is there any evidence to suggest that the true mean weight is not 45 pounds at a 5% significance level?

Calculate the test statistic

Calculate the p-value.

Write the complete four steps of the hypothesis test below. The work for all parts will be at the end of the question.

c) Calculate the 95% confidence interval for the mean.

d) Explain why parts b) and c) state the same thing. That is, what in part b) is consistent with what in part c)?

e) Is there strong evidence for your decision of "reject the null hypothesis" or "fail to reject the null hypothesis"? Please explain your answer using the results from both the hypothesis test and the confidence interval.

Answer 1

Solution:-

a) z distribution should be used for statistical procedures regarding the mean.

b)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 45
Alternative hypothesis: u 45

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), and the z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 0.77611

z = (x - u) / SE

z = 2.062

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z statistic less than -2.062 or greater than 2.062.

Thus, the P-value = 0.0392

Interpret results. Since the P-value (0.0392) is less than the significance level (0.05), we have to reject the null hypothesis.

c) 95% confidence interval for the mean is C.I = ( 45.08, 48.121).

C.I = 46.6 + 1.96 × 0.77611

C.I = 46.6 + 1.52118

C.I = ( 45.08, 48.121)

d) The parts b) and c) state the same thing because both are using the same confidence interval and both says that "The Dover, the largest block in a certain collection, is used primarily for residential retaining walls, and is manufactured to weigh 45 pounds".

e)  There is strong evidence for our decision of "fail to reject the null hypothesis".