Question 1
The times taken to assemble a car in a manufacturing plantfollow a normal distribution with a mean of 20 hours and a standard deviation of 2 hours. Use this information to answer the following questions. Show your working, including an appropriate diagram.
a. Find the probability that a randomly selected car takes between 21 and 24 hours to assemble.
b. Find the probability that the average assembly time for a randomly selected sample of 5 cars manufactured in the plant will be longer than 22 hours.
c. 69% of new cars purchased in Australia have automatic transmission. Find the probability that less than 40 new cars from a random sample of 50 have automatic transmission.
Question 2.
In 2013, a study of 50 cruise ships was undertaken to investigate the variables which determine the crew size of a cruise ship. For each of the 50 cruise ships, information was recorded on their most recent cruise.
Some of the variables recorded on each cruise ship are described below.
Variable Name Variable Description
Ship Name of cruise ship
Age Age of the cruise ship in years as of 2013
Cabins Number of cabins
Passengers Number of passengers on most recent cruise
Crew Number of crew on most recent cruise
The following output was constructed from information recorded on the age and the crew size of the 50 cruise ships in the study. Consider this output for parts a. to f.
Regression Analysis: Crew versus Age
Model Summary
S R-sq R-sq(adj) R-sq(pred)
235.954 49.67% 48.62% 45.38%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 1301.3 87.2 14.92 0.000
Age -35.74 5.19 -6.88 0.000 1.00
Regression Equation
Crew = 1301.3 - 35.74 Age
a. Comment on the relation between the age of a cruise ship and the number of crew employed on the ship:
b. Did the oldest cruise ship have the largest crew size?
c. What was the approximate age and crew size of the oldest cruise ship?
d. 6 of the cruise ships were 12 years old. What was the approximate crew size of the 12 year old ship with the smallest crew size?
e. The 12 year old cruise ship with the smallest crew size had the largest residual. Calculate the approximate value of this residual, using your results from part d.
f. Write down one reason (referring specifically to relevant part of the output on the previous page) why a linear model may not be a good model for predicting the number of crew required on a cruise ship from the age of the cruise ship:
Question 3
Using appropriate parts of the following output which was constructed using the results of this study to carry out a hypothesis test in the space provided on the following pageto answer this research question:
Descriptive Statistics: PainScoreAfter_Back, PainScoreAfter_Migraine
Variable N Mean SE Mean StDev Minimum Median Maximum
PainScoreAfter_Back 52 5.933 0.155 1.116 3.500 6.000 8.500
PainScoreAfter_Migraine 63 4.999 0.118 0.938 3.000 5.000 7.000
Question 4
a. The file, PainScores.mtw, which is available on iLearn, contains some of the data from the study described on page 6. Use these data tocarry out an appropriate hypothesis test to answer this research question above.
b. Copy and paste appropriate Minitab output for this test, along with appropriate graphical summaries onto the following page. All Minitab output should be neatly presented and clearly labelled. Marks will be deducted for summaries which do not have appropriate titles and labels.
c. Write a report addressing the research question above on the page provided.Refer to the document ‘A Guide to Report Writing' and, in particular, to the section headed ‘A Short Guide to Report Writing for STAT170 students' which is provided on iLearn. Your report should be based on the results of an appropriate hypothesis tests as directed in this guide. Your reportnot exceedone A4 page and should be word-processed and presentedon the page provided. It should include the following headings:
Introduction
Methods
Results
Conclusion