Question

In recent years more people have been working past the age of 65. In 2005, 27% of people aged 65–69 worked. A recent report from the Organization for Economic Co-operation and Development (OECD) claimed that the percentage working had increased (USA Today, November 16, 2012). The findings reported by the OECD were consistent with taking a sample of 600 people aged 65-69 and finding that 180 of them were working.

a. Develop a point estimate of the proportion of people aged 65-69 who are working (to 2 decimals).

b. Set up a hypothesis test so that the rejection of H0 will allow you to conclude that the proportion of people aged 65-69 working has increased from 2005.

c. Conduct your hypothesis test using α=.05. p-value=?

d. What is your conclusion? ( has the proportion of people increased or not)

2. An airline promotion to business travelers is based on the assumption that no more than two-thirds of business travelers use a laptop computer on overnight business trips. a. State the hypotheses that can be used to test the assumption.

ho=

ha=

b. What is the sample proportion from an American Express-sponsored survey that found 363 of 543 business travelers use a laptop computer on overnight business trips (to 4 decimals)?

c. What is the p-value (to 4 decimals)?

d. Using = .05, can you conclude that the proportion of business travelers who use a laptop computer on overnight business trips is greater than two-thirds? (yes or no)

Answer 1

Answer Date: 22/04/2020 Solution 1 The point estimate of the proportion of people aged 65-69 who are working is, Pot 180 600 = 0.30 The point estimate of the proportion of people aged 65-69 who are working is 0.30. b) To test the hypothesis is that the proportion of people aged 65-69 working has increased 27% at 5% significance level.

The null and alternative hypothesis is, H:p= 0.27 H:p> 0.27 c) The z-test statistics is, By using TI-84 calculator, find z-test statistics with the help of following steps: 1) Import the data. Select TESTS from Stat menu. 3) Select 1-Proportions Z Test from TESTS variables. Enter PO, x, n and select Alternative from 1-Proportions Z Test. Select Alternative from Hypotheses. Press Calculate.

1-PropZTest prop.27 z=1.655211777 P=.0489467549 P=.3 n=6.a From the TI-84 calculator output, the z-test statistics is 1.66. The p-value for this test is, From the TI-84 calculator output, the p-value for this test is 0.0489 Decision The conclusion is that the p-value in this context is less than 0.05 which is 0.0489, the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the proportion of people aged 65-69 working has increased 27%. The result is statistically significant.

Solution 2 a) To test the hypothesis is that the proportion of business travelers who use a laptop computer on overnight business trips is greater than two-thirds at 5% significance level. The null and alternative hypothesis is, Ho:p <0.67 Ha:p>0.67 b) The sample proportion from an American Express-sponsored survey that found 363 of 543 business travelers use a laptop computer on overnight business trips is, 363 543 = 0.6685

The sample proportion from an American Express-sponsored survey that found 363 of 543 business travelers use a laptop computer on overnight business trips is 0.6685 - The p-value for this test is, 1) By using TI-84 calculator, find p-value with the help of following steps: Import the data. Select TESTS from Stat menu. Select 1-Proportions Z Test from TESTS variables. Enter PO, x, n and select Alternative from 1-Proportions Z Test. Select Alternative from Hypotheses. Press Calculate. 1-PropZTest prop.66666 z=.090879024 P=.4637978706 n=543

From the TI-84 calculator output, the p-value for this test is 0.4637). d) Decision The conclusion is that the p-value in this context is higher than 0.05 which is 0.4637, so the null hypothesis is not rejected at 5% level of significance. There is not sufficient evidence to indicate that the proportion of business travelers who use a laptop computer on overnight business trips is greater than two-thirds. The result is not statistically significant.