Week 9, Chapter 9 Homework

| June 10, 2016

Week 9, Chapter 9

Homework requiring Excel, PhStat2 must be submitted in that format via your Excel spreadsheets. Either software or manual calculations may be used for the following problems requiring computation.

Problems: 9-3 (a and b only), 9-5, 9-13, 9-32, 9-35,9-54, 9-78 (not calculating any values here, this is a conceptual question).

Problem 9-3: (a and b only):

Provide the relevant critical value(s) for each of the following circumstances:

HA: µ > 13, n = 15, σ = 10.3, α = 0.05
HA: µ ≠ 21, n = 23, s = 35.40, α = 0.02
You will have to provide the critical value using either the normal (z) or t distribution or both. Some more detailed explanation follows:

A critical value is a “cut-off” point, or boundary that begins the rejection region. That is, if your calculated test statistic falls in the rejection region, you can reject the null hypothesis at a level of significance determined by the critical value. You can have a critical value on the right side of the distribution, the left side of the distribution, or both sides. So how do you determine what your critical value is?
Step 1: What is your alternative hypothesis? This determines where your critical value is. If your Ha is that u > some value, then you have a right-tailed test, and your critical value is on the right. If Ha is u Z-test for the mean, sigma known.

Problem 9-13:

The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750.

State the appropriate null and alternative hypotheses.
Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the critical value (state in dollars)?
Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis?
Referring to your answer in part c, which of the two statistical errors might have been made in this case? Explain.
You will first need to identify the critical (z) value, and then solve for the sample mean.

Part a asks you to identify the null and alternative hypothesis. Remember that the alternative hypothesis is usually what they are trying to “prove”, “test”, or “claim”.
Part b: use formula solving for the sample mean.
Part c: does your sample value fall in the region of rejection? If so, reject the null hypothesis. If not, you will not reject it.
Part d: Every time you do a hypothesis test, you can make one of two types of errors. Type I and Type II errors
Problem 9-32:

A major issue facing many states is whether to legalize casino gambling. Suppose the governor of one state believes that more than 55% of the state’s registered voters would favor some form of legal casino gambling. However, before backing a proposal to allow such gambling, the governor has instructed his aides to conduct a statistical test on the issues. To do this, the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state. Of these 300 voters, 175 actually favored legalized gambling.

State the appropriate null and alternative hypotheses.
Assuming that a significance level of 0.05 is used, what conclusion should the governor reach based on these sample data? Discuss.
This is a straightforward application of equation or, you can use PHStat: One-sample tests > z-test for the proportion.

Problem 9-35:

A Washington Post-ABC News poll found that 72% of people are concerned about the possibility that their personal records could be stolen over the Internet. If a random sample of 300 college students at a Midwestern university were taken and 228 of them were concerned about the possibility that their personal records could be stolen over the Internet, could you conclude at the 0.025 level of significance that a higher proportion of the university’s college students are concerned about Internet theft than the public at large? Report the p-value for this test.

Can be solved with manual calculations. If using PhStat: One-Sample Tests > Z-Test for the Proportion.

Problem 9-54:

For each of the following situations, indicate what the general impact on the Type II error probability will be:

The alpha level is increased.
The “true” population mean is moved farther from the hypothesized population mean.
The alpha level is decreased.
The sample size is increased.

Problem 9-78:

The Oasis Chemical Company develops and manufactures pharmaceutical drugs for distribution and sale in the United States. The pharmaceutical business can be very lucrative when useful and safe drugs are introduced into the market. Whenever the Oasis research lab considers putting a drug into production, the company must actually establish the following sets of null and alternative hypotheses:

Set 1 Set 2

H0:The drug is safe. H0:The drug is effective.

HA: The drug is not safe. HA: The drug is not effective.

Take each set of hypotheses separately,

Discuss the considerations that should be made in establishing alpha and beta.
For each set of hypotheses, describe what circumstances would suggest that a Type I error would be of more concern.
For each set of hypotheses, describe what circumstances would suggest that a Type II error would be of more concern.
Same concepts as in problem 9-54, just a different application.

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