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# 1) Twenty-five factory workers were asked how many vacation days they take a year. The average of the sample was 22.85 days, and the standard...

1) Twenty-five factory workers were asked how many vacation days they take a year. The average of the sample was 22.85 days, and the standard deviation was 5.80 days. In the past HR uses an average of 25 vacation days per worker in order to make available man-hour and payroll predictions. Is there evidence to show that the number of vacation days decreased over the past year? Use alpha=.05
State the hypothesis, the test statistic, the conclusion, (what you are accepting or rejecting) and make sure you answer the question.

2) A survey conducted by USA today showed that 118 of 250 investors owned some real estate. In the past it showed that 45% of investors owned some real estate. Has the number of investors that own some real estate increased? Use alpha =.01
State the hypothesis, the test statistic, the conclusion, (what you are accepting or rejecting) and make sure you answer the question.

3) A manufacturer has received complaints that aging production equipment is forcing workers to work overtime in order to meet production quotas. Historically, the average hours worked per week at the company is normally distributed, with a mean of 40 hours and a standard deviation of 7.5 hours. If a sample of 30 workers found an average work week of 45 hours, conduct a hypothesis test to determine if there is significant evidence (at a 5 percent level of significance) that the length of the average work week has increased.
State the hypothesis, the test statistic, the conclusion, (what you are accepting or rejecting) and make sure you answer the question.

4) A coin that is balanced should come up heads half the time in the long run. The population for coin tossing contains the results of tossing the coin forever. The parameter p os the probability of a head, which is the proportion of all tosses that give a head. A coin is tossed 4040 times and gives 2085 heads. Is the coin biased? Use alpha =.05
State the hypothesis, the test statistic, the conclusion, (what you are accepting or rejecting) and make sure you answer the question.

5) Assuming that this is a standard coin, what type of Error did you commit in #4 and why?

6) A new breakfast cereal Frosted Corn is test marketed for one month. The total sales for the first 9 quarters indicate an average of \$8350, with a standard deviation of \$1840. Based on a cost-profit analysis, production of Frosted Corn will be discontinued if the sample average of the first 9 quarters falls below \$9000 with statistical significance. Does the data indicate production will be stopped?
Use alpha =.05
State the hypothesis, the test statistic, the conclusion, (what you are accepting or rejecting) and make sure you answer the question.

7) A Michigan automobile insurance company would like to estimate the average size of an accident claim for the fiscal year 2009. A random sample of 20 accidents claims yielded an average of \$1600 with a standard deviation of \$800. The national average claim for the industry is \$1500. Does the sample indicate that the Michigan average is different from the national average? Use alpha =.10
State the hypothesis, the test statistic, the conclusion, (what you are accepting or rejecting) and make sure you answer the question.

8) Researchers concerned if doctors were consistently adjusting dosages for weight of elderly patients studied 2000 prescriptions. They found that for 600 of the prescriptions, the doctors failed to adjust the dosages. In the past researcher found that 33% of doctors were consistently adjusting dosages for weight of elderly patients. Has the number of doctors who were consistently adjusting dosages for weight of elderly patients decreased over the past few years? Use alpha =.01
State the hypothesis, the test statistic, the conclusion, (what you are accepting or rejecting) and make sure you answer the question.

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Solution: 1
Solution: 2
Reject the null hypotheseis if calculated Z &gt; Zα/2
Solution: 3
The length of the average work week has not increased
Solution: 4
Reject the null hypotheseis if...

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