1703 Final Review

1703 Final Review
1. Observing other students in your classroom, determine if the following are qualitative or quantitative.
(a) Students with brown hair.
(b) The height of students in the classroom.
2. The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter
of 0.255 inches. A random sample of 20 shafts has an average diameter of 0.2545 inches and a standard
deviation of 0.001 inch. The probability of a Type I error is 0.05. Assume the data are normally
distributed.
(a) Set up the hypotheses.
(b) Determine the test statistic.
(c) Determine the critical value.
(d) Make a decision.
(e) State your conclusion in terms of the problem.
(f) Determine a 95% confidence interval for the problem.
(g) Interpret this interval.
1
3. Answer the following.
(a) What is Type I error?
(b) What is Type II error?
4. The average 20- to 29-year-old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while
the average 20- to 29-year-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who
is relatively taller, a 67-inch man or a 62-inch woman?
5. Suppose the distribution of monthly earnings from all people who possess a bachelor’s degree is known
to be bell-shaped and symmetric with a mean of $2116 and a standard deviation of $455. Answer the
following:
(a) What percentage of individuals with a bachelor’s degree earn less than $1661 per month?
(b) What percentage of individuals with a bachelor’s degree earn more than $1206 per month?
(c) What percentage of individuals with a bachelor’s degree earn between $2116 and $3481 per month?
2
6. The cost of maintenance of shipping tractors seems to increase with the age of the tractor. Observe
the data and excel output on the next page and answer the following questions.
Age (yr)
4.5
4.5
4.5
4.0
4.0
4.0
5.0
5.0
5.5
5.0
0.5
0.5
6.0
6.0
1.0
1.0
1.0
6 Months Cost ($)
619
1049
1033
495
723
681
890
1522
987
1194
163
182
764
1373
978
466
549
(a) Observe the scatterplot. Does there appear to be a linear relationship between the age of the
tractor and the cost of the maintenance of shipping the tractors?
(b) Give the coefficient of determination.
(c) Define what this value represents.
(d) Give the correlation coefficient.
(e) What is the linear regression equation for the data?
(f) What is the predicted cost of maintenance of shipping a tractor that is 2.5 years old?
3
Output for Problem 6.
Output for Problem 7.
4
7. Use the following data from Statistical Abstract of the United States (2003) to predict the number of
college graduates with bachelor’s degrees in the year 2005. Use the output provided on the previous
page. (Use the time period not the actual year in your calculations.)
Time Period
Year
Graduates (millions)
1
1996
1.16
2
1997
1.17
3
1998
1.18
4
1999
1.20
5
2000
1.24
(a) What is the correlation coefficient?
(b) Give the coefficient of determination, and interpret it.
(c) What is the linear regression equation for the data?
(d) What is the slope? Explain what it means in terms of the problem.
(e) Based on the equation, how many graduates could be predict in 1999?
(f) What is the residual for the number of graduates in the year 1999?
(g) Is the observed value above or below the predicted value from part (f)?
5
8. In 1990, the mean height of women 20 years of age or older was 63.7 inches with a standard deviation of
0.8 inches based on data obtained from the Centers for Disease Control and Prevention’s Advance Data
Report, No. 347. Suppose that a random sample of 45 women who are 20 years of age or older today
results in a mean height of 63.9 inches. Use the clsasical approach for α = 0.10 level of significance.
(a) Set up the hypotheses.
(b) Determine the test statistic.
(c) Find the p-value.
(d) Make a decision.
(e) State your conclusions in terms of the problem.
(f) Compute a 90% confidence interval for this problem.
(g) Interpret the interval in part (g).
9. Explain the Law of Large Numbers.
6
10. Given the following sample data, answer the questions below:
12 15 14 9 14 18 10
(a) Find the mean.
(b) Find the median.
(c) Find the mode.
(d) Find the variance.
(e) Find the standard deviation.
11. An insurance company is reviewing its current policy rates. When originally setting the rates they
believed that the average claim amount was $1,800. They are concerned that the true mean is actually
higher than this, because they could potentially lose a lot of money. Define a Type II Error for this
scenario.
7
12. An English placement exam was given to incoming students. The distribution of exam scores is
approximately normal with a mean of 82 and a standard deviation of 5.
(a) What is the probability of scoring less than 70?
(b) What is the probability of scoring higher than 90?
(c) What is the probability of scoring between 75 and 85?
13. We would like to estimate the mean teacher’s salary in the Chapel Hill school district, with 99%
confidence, to an accuracy within $2000. We know the standard deviation of teacher’s salaries in this
area is $6000. What sample size is necessary to estimate teacher’s salaries?
8
14. Determine the shape of the histogram below. Then, state where the mean and median would fall on
the histogram.
15. Below, match the scatter diagram with the correlation coefficient.
(1) 0.00
(2) +0.85
(3) -0.98
(4) +0.98
(5) -0.85
(6) 0.00
16. (a) Determine the right-tailed t critical value for an α of 0.10 and 14 degrees of freedom.
That is, t0.10 (14) =.
(b) What is your conclusion if the test statistic is t = 2.27?
17. Trying to encourage people to stop driving to campus, the university claims that on average it takes
people 30 minutes to find a parking space on campus. I dont think it takes so long to find a spot.
Define a Type I Error for this scenario.
9
18. Many people sleep in on the weekends to make up for “short nights” during the work-week. The Better
Sleep Council reports that 61% of us get more than seven hours of sleep per night on the weekend. A
random sample of 350 adults found that 225 had more than seven hours each night last weekend. Test
the claim that 61% of people get seven hours of sleep per night on the weekend.
(a) Set up the hypotheses.
(b) State the assumptions necessary for this test to be valid. Check these assumptions.
(c) Determine the test statistic.
(d) Find the p-value.
(e) Make a decision.
(f) State your conclusions in terms of the problem.
(g) Compute a 95% confidence interval for this problem.
(h) Interpret the interval in part (g).
10