Problem: The "cold start ignition time" of an automobile engine is investigated by a gasoline manufacturer. The following 8 times (in seconds) were obtained for a test vehicle:

1.75, 1.92, 2.62, 2.35, 3.09, 3.15, 2.53, 1.91

A Construct and interpret the 95% confidence interval for the population mean start ignition time of an automobile engine.

B Test at 0.05 significance level whether the population mean start ignition time is below 2.9 
seconds. Include the hypotheses, the test statistic, the p-value, test decision 
and conclusion in the context of the problem.

C . Does the confidence interval in the output support your statistical decision? Explain.

D . Construct a Normal Probability Plot of the data. In your opinion, does the graph support an assumption of normality? Explain.

E . Perform a Shapiro-Wilk test of normality. State hypothesis, p-value and conclusion. Did this support your decision in part (d) based on the normality plot?

F . What test decision error could you have made and provide an explanation of this error in context of the problem.

G . Include a copy of your R-code, test output, and normal probability plot.

Problem: The life (in hours) of 75-watt light bulbs is under study. A random sample of 35 light bulbs produces a mean of 1014 hours and a standard deviation of 25 hours. (NOTE: Remember you will need the BSDA library to be able to run the R code.)

1. Test whether the population average life of 75-watt light bulbs is above 1000 hours at a 0.10 level of significance. Include the hypotheses, the test statistic, the p-value, test decision and conclusion in the context of the problem.
2. Can we safely assume the sample mean is approximately normal? Explain.
3. Why can't we construct a normal probability plot to support this decision in part (b)?
4. What test decision error could you have made and provide an explanation of this error in context of the problem.
5. Include a copy of your R-code and test output.

QUESTION 3

A health magazine conducted a survey on the drinking habits of US young adults (ages 21-35). On the question "Do you drink beer, wine, or hard liquor each week?" 985 of the 1516 adults interviewed said "yes".

1. Test at 0.02 significance level whether the population proportion of US young adults who drink beer, wine, or hard liquor on a weekly basis is significantly different from 65%. Include the hypotheses, the Z-test statistic, the p-value, test decision and conclusion in the context of the problem.
2. Do you believe your results are valid? Explain.
3. What test decision error could you have made and provide an explanation of this error in context of the problem.
4. Include a copy of your R-code and test output.

QUESTION 4

Read into R the BearsData set. This data includes information on 50 bears, 15 of which were identified as Female and 35 as Male.

1. Test whether there is a difference in Weight (in pounds) between the Sex of bears at a 0.05 level of significance. Include the hypotheses, the test statistic, the p-value, test decision and conclusion in the context of the problem.
2. Do you believe the test results are valid? Explain.
3. What test decision error could you have made and provide an explanation of this error in context of the problem.
4. Include a copy of your R-code and test output

QUESTION 5

To compare corrosion-resistance properties of two types of materials, Type A and Type B, were used in underground pipelines. Specimens of both types are buried in soil for a 2-year period and the maximum penetration (in mils) for each specimen is measured. The resulting sample statistics for each type are as follows:

Type A: mean = 0.49 sd = 0.19 n = 42

Type B: mean = 0.36 sd = 0.16 n = 42

1. Test whether the corrosion-resistance properties differ between the two material types at a 0.05 level of significance. Include the hypotheses, the test statistic, the p-value, test decision and conclusion in the context of the problem.
2. Do you believe the test results are valid? Explain.
3. What test decision error could you have made and provide an explanation of this error in context of the problem.
4. Include a copy of your R-code and test output.

QUESTION 6

A study was conducted to see whether two types of cars, A and B, took the same time to parallel park. Seven drivers were randomly obtained and the time required for each of them to parallel park (in seconds) each of the 2 cars was measured. The results are listed below in order of driver (e.g. the first listing for A and B are driver 1; the second listing driver 2; etc.)

Car A: 19, 21.8, 16.8, 24.2, 22, 34.7, 23.8

Car B: 17.8, 20.2, 16.2, 41.4, 21.4, 28.4, 22.7

1. Explain why this is a paired test and not a two sample test.
2. Test whether the there is a difference in mean parallel parking time of the two cars at a 0.05 level of significance. Include the hypotheses, the test statistic, the p-value, test decision and conclusion in the context of the problem.
3. Do you believe the test results are valid? Explain.
4. What test decision error could you have made and provide an explanation of this error in context of the problem.
5. Include a copy of your R-code and test output.

QUESTION 7

The summary data of the differences (Car B minus Car A) are as follows:

Differences: mean = 0.8286 sd = 7.491 n = 7

Use this information to rerun the test from Question 6b. Are your results the same, excluding rounding error? Include a copy of your R code and test output.

Price: $33.55

Solution: The downloadable solution consists of 14 pages, 1955 words and 12 charts.
Deliverable: Word Document