**Subject Mathematics General Statistics**

## Question

2. The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 16 people reveals the mean yearly consumption to be 60 gallons with a standard deviation of 20 gallons. Assume the population distribution is normal.

• What is the value of the population mean? What is the best estimate of this value?

• Explain why we need to use the t distribution. What assumption do you need to make?

• For a 90% confidence interval, what is the value of t?

• Develop the 90% confidence interval for the population mean.

3. Would it be reasonable to conclude that the population mean is 63 gallons?

Ms. Maria Wilson is considering running for mayor of the town of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals that 300 would support her in the November election.

• Estimate the value of the population proportion.

• Develop a 99% confidence interval for the population proportion.

• Interpret your findings.

4. The estimate of the population proportion is to be within plus or minus .10, with a 99% level of confidence. The best estimate of the population proportion is .45. How large a sample is required?

5. A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level.

H0: μ ≥ 220

H1: μ <220

6. At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $80 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $9.95. Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $84.85. At the .01 significance level, can Ms. Brigden conclude that her daily tips average more than $80?

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