Stas assignment

PART 1: Confidence Intervals (#1 – 3)

1) To estimate the mean size of maple trees in a certain area of the Adirondacks. A sample of 12 maple tree heights is collected. (Assume that the population of tree heights is normally distributed)

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a) Create a 95% confidence interval for the population mean of maple tree

heights.

b) Create a 98% confidence interval for the population mean of maple tree

heights.

2) Suppose a simple random sample of 20,000 Americans were surveyed and 8,600 of them said they have blue colored eyes.

a) Create a 90% confidence interval estimator for the population proportion of Americans that have blue colored eyes.

What is the minimum sample size that would be required to estimate the population’s proportion

b) Create a 98% confidence interval for the population mean of maple tree with an error of .025 at a 95% level of confidence? (Note: assume we have a preliminary estimate of )

3) Estimating Fuel Efficiency:

a) In order to determine the fuel efficiency for the Toyota Corolla a SRS of 36 Corollas were driven yielding a sample mean of 34.3 miles per gallon and a sample standard deviation of 2.4 miles per gallon create a 99% confidence interval estimate for the population mean miles per gallon for the Toyota Corolla.

b) What is the minimum sample size that would be required to estimate the population’s mean with an error of 0.1 miles per gallon at a 90% level of confidence? (Assumes = 2.4)

PART 2: Hypothesis Testing (#4 – 6)

For each of the questions of Part 2 you MUST show each of the four steps below to obtain full credit:

A) State the null and alternate hypothesis.

B) Determine the rejection region (use either classical approach or p value approach).

For example “if , then reject ” or “if , then reject ”

C) Calculate the Test Statistic and determine the p-value of the test.

D) Conclude either “Reject ” or “Do not reject”

You must show work to obtain credit. Each question will also have a YES/NO option. Please circle the choice that answers the question correctly based on your analysis.

4) A Tire Company has created a new type of rubber that they believe could increase the tread life of their tires. In the past the population mean tread life of their tires was 50,000 miles. To test this hypothesis, a SRS of 30 tires were tested that had a sample mean tread life of 50,480 miles and a sample standard deviation of 1,200 miles.

Does this sample provide sufficient evidence to suggest that the new rubber has increased mean tread life at the 5% Significance Level? (Circle either Yes or No).

YES NO

Please show the four steps of your analysis in the space provided below…

the past the population mean tread life of their tires was 50,000 miles. To test this hypothesis, a SRS of 30 tires were tested that had a sample mean tread life of 50,480 miles and a sample standard deviation of 1,200 miles.

Does this sample provide sufficient evidence to suggest that the new rubber has increased mean tread life at the 5% Significance Level? (Circle either Yes or No).

YES NO

Please show the four steps of your analysis in the space provided below…

5) The National Center for Health Statistics reports that the population mean systolic blood pressure for males 35 to 44 years of age is exactly 130. The medical director of a large company believes that the executives at her company are different from the population. To gather evidence, she collects a SRS of 11 medical records of male executives in this age group. (Assume that the population of systolic blood pressures is normally distributed)

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Does the data suggest that the average blood pressure of male executives is different from the population mean at the 1% significance level? (Circle either Yes or No).

YES NO

Please show the four steps of your analysis in the space provided below…

6) It is believed that less than 50% of American adults eat breakfast every day. To test this claim a researcher surveys SRS of 850 American adults where 400 of them said that they ate breakfast every day.

Does this sample evidence suggest that less than 50% of American adults eat breakfast everyday at the 10% significance level? (Circle either Yes or No).

YES NO

Please show the four steps of your analysis in the space provided below…