Question

Previous Page Next Page Page 6 of 9 Question 6(1.5 points) The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available," is to be investigated at the 0.02 level of significance. If 74 out of the 200 workers sampled said they would return to work, what is our decision? Do no reject the null hypothesis because -0.866 lies in the region between 0 and -2.33 Reject the null hypothesis because 37% is less than 40% Do not reject the null hypothesis because 37% lies in the area between 0% and 40% Do net reject the mull ypotbess because 50 866 te in he region benween 0and 2 ss Previous Page Next Page Page 6 of 9

Answer 1

Option A is correct

Explanation

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

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

  Null hypothesis: P = 0.40

  Alternative hypothesis: P ≠ 0.40

  Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.
• Formulate an analysis plan. For this analysis, the significance level is 0.02.
• Analyze sample data. Using sample data, we calculate the standard deviation (σ) and compute the z-score test statistic (z).

  σ = sqrt[ P * ( 1 - P ) / n ]

  σ = sqrt [(0.40 * 0.60) / 200]

  σ = 0.03464

  z = (p - P) / σ = (0.37 - 0.40)/ 0.03464 = -0.8661

  where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

  Since we have a two-tailed test, the P-value is the probability that the z-score is less than -0.8661 or greater than 0.8661.

  We use the Normal Distribution Calculator to find P-value. Thus, the P-value is 0.38649 .
• Interpret results. Since the P-value (0.38649) is greater than the significance level (0.02), we cannot reject the null hypothesis.