The decision rule in terms of critical value

Chapter 9 (11-27)

Put answers in excel

9-3:

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

1.  >13, n= 15,σ =10.3,ὰ =0.05
2.  µ ≠ 21, n=23, s=35.40,ὰ=0.02

Problem 9-5:

For the following hypothesis test:

µ= 200

: µ≠ 200

        ὰ= 0.01

With n = 64, σ = 9, and x= 196.5, state

a.       The decision rule in terms of critical value of the test statistic

b.      The calculated value of the test statistic

c.       The conclusion

Problem 9-13:

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

a.       State the appropriate null and alternative hypotheses.

b.      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 (stated in dollars)?

c.       Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis?

d.      Referring to your answer in part c, which of the two statistical errors might have been made in this case? Explain.

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 gambling. However, before backing a proposal to allow such gambling, the governor has instructed his aides to conduct a statistical test on the issue. 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.

a.       State the appropriate null and alternative hypotheses.

b.      Assuming that a significance level of 0.05 is used, what conclusion should the governor reach based on these sample data? Discuss.      

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.    

Problem 9-54:

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

a.       The alpha level is increased.

b.      The true population mean is moved farther from the hypothesized population mean.

c.       The alpha level is decreased.

d.      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. Whatever 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

: The drug is safe.                                      : The drug is effective

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

Take each set of hypotheses separately.

a.       Discuss the considerations that should be made in establishing alpha and beta.

b.      For each set of hypotheses, describe what circumstances would suggest that a Type I error would be of more concern.

c.       For each set of hypotheses, describe what circumstances would suggest that a type II error would be of more concern.