# Q 11, Consider the following hypothesis test:                                  Ho: µ =15                                   Haµ≠ 15A sample of 50 provided a sample mean of 14.15. The population standard is3Compute the value of the test statistic.What is the p- value?At α=.05,what your conclusionWhat is the rejection rule using the critical value? What is your conclusion?ApplicationsP282 Q27, which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli and rice bought at the grocery store is \$ 13.04 (Money, msn website, November 7, 2012).A sample of 100 neighborhood restaurants showed a mean price of \$12.75 and a standard deviation of \$2 for a comparable restaurant meal.Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than the fixing a comparable meal at home.Using the sample from the 100 restaurants, what is the p-value?At α=.05, what is your conclusion?Repeat the preceding hypothesis test using the critical value approach?   P287 Q37 The U.S Bureau of labor statistics report that 11.3% of U.S workers belong unions (BLS website January 2014) .suppose a sample of 400 U.S workers is collected in 2014 to determine whether union efforts to organize have increased union membership.Formulate the hypotheses that can be used to determine ehether union membership increased in 2014.If the sample results show that 52 of the workers belonged to unions what is the p-value for your hypothesis test?At α=.05 what is your conclusion?   P 300 Q61 At western university the historical mean of scholarship examination scores for freshman application is 900. A historical population standard deviation α=180 is assumed known .Each year the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman application has changed.State the hypotheses.What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean x =935?Use the confidence interval to conduct a hypothesis test. Using α=.05, what is your conclusion?What is the p-value?

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Q 11, Consider the following hypothesis test:

Ho: µ =15

Haµ≠ 15

A sample of 50 provided a sample mean of 14.15. The population standard is3

1. Compute the value of the test statistic.
2. What is the p- value?
4. What is the rejection rule using the critical value? What is your conclusion?

Applications

P282 Q27, which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli and rice bought at the grocery store is \$ 13.04 (Money, msn website, November 7, 2012).A sample of 100 neighborhood restaurants showed a mean price of \$12.75 and a standard deviation of \$2 for a comparable restaurant meal.

1. Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than the fixing a comparable meal at home.
2. Using the sample from the 100 restaurants, what is the p-value?
3. At α=.05, what is your conclusion?
4. Repeat the preceding hypothesis test using the critical value approach?

P287 Q37 The U.S Bureau of labor statistics report that 11.3% of U.S workers belong unions (BLS website January 2014) .suppose a sample of 400 U.S workers is collected in 2014 to determine whether union efforts to organize have increased union membership.

1. Formulate the hypotheses that can be used to determine ehether union membership increased in 2014.
2. If the sample results show that 52 of the workers belonged to unions what is the p-value for your hypothesis test?
3. At α=.05 what is your conclusion?

P 300 Q61 At western university the historical mean of scholarship examination scores for freshman application is 900. A historical population standard deviation α=180 is assumed known .Each year the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman application has changed.

1. State the hypotheses.
2. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean x =935?
3. Use the confidence interval to conduct a hypothesis test. Using α=.05, what is your conclusion?
4. What is the p-value?

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Step 1

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Step 2

1.

Computation of test statistic:

In this context, the population mean is 15. Therefore, H0:µ=15 Vs H1:µ≠15. It is given that it is assumed that X has a normal distribution and σ = 3.Here, the sample mean, x-bar is 14.15. Population mean, µ is 15.Population standard deviation, σ = 3. Sample size, n is 50. The test statistic for z-test is calculated as -2.003 from the calculations given below.

Step 3

2.

The P-value for the z-test can be obtained using the excel formula,=NORM.S.DIST(-2.003,TRUE)”. Thus, the P-value f...

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