Question

Asked Dec 23, 2019

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*Q 11, Consider the following hypothesis test:*

** H _{o}: µ =15**

** H _{a}µ≠ 15**

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

- Compute the value of the test statistic.
- What is the p- value?
- At α=.05,what your conclusion
- 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.**

- 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?

Step 1

**Note:** Hey, since there are multiple questions posted, we will answer 1^{st} three parts of 1^{st} question. If you want any specific question or specific parts to be answered then please submit that question only or specify the question number in your message.

Step 2

**1.**

**Computation of test statistic:**

In this context, the population mean is 15. Therefore, H_{0}:µ=15 Vs H_{1}: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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