1. (6 points) According to the U.S. National Center for Health Statistics, the mean height of 18 -24 year old American males is 69.7 inches. Assume the heights are normally distributed with a standard deviation of 2.7 inches.
Fill in the following blanks:
a. About 68.26% of 18 -24 year old American males are between ______ and ______ inches tall.
b. About 95.44% of 18 -24 year old American males are between ______ and ______ inches tall.
c. About 99.74% of 18 -24 year old American males are between ______ and ______ inches tall.
2. (6) A study of the effect of college education on job satisfaction was conducted. A contingency table is presented below:
Attended College Did not Attend Total
Satisfied with job 325 186 511
Not satisfied with job 190 369 559
Total 515 555 1070
If you were to randomly sample an individual from this population, find the probability of selecting an individual who
a. is satisfied with job
b. did not attend college knowing that the individual was not satisfied with job
c. is satisfied with job and did not attend college
3. (6) Each year a large university collects data on average beginning monthly salaries of its business school graduates. A random sample of 125 recent graduates with bachelor’s degrees in marketing has a mean starting monthly salary of $1635 with a standard deviation of $288. Use these data to obtain an estimate for the mean starting monthly salary of all recent graduates with bachelor’s degrees in marketing from this university. Assume that you want the estimate to be incorrect at most 10 percent of the time.
4. (7) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program and their current GPAs.
Entering GPA Current GPA
a. Test the appropriate hypotheses and determine the linear regression model for the data.
b. Graph the regression model.
c. How well does the model represent the relationship between the variables?
d. What does the slope for the regression model represent?
e. Use the regression equation to predict the current GPA of a student with an entering GPA of 3.6.
5. (6) Classify the following studies as descriptive or inferential and explain your reasons:
a. A study on stress concluded that more than half of all Americans older than 18 have at least “moderate” stress in their lives. The study was based on responses of 34,000 households to the 1985 National Health Interview Survey.
b. A report in a farming magazine indicates that more than 95% of the 400 largest farms in the nation are still considered family operations.
6. (7) The age distribution of students at a community college is given below:
Age in Years Number of Students (f)
Under 21 4946
21 – 25 4808
26 – 30 2673
31 – 35 29036
Over 35 525
Suppose a student is selected at random. Let
A = the event the student is under 21
B = the event the student’s age is between 21 and 25
C = the event the student’s age is between 26 and 30
D = the event the student’s age is between 31 and 35
E = the event the student’s age is over 35
a. Find P (B)
b. Find P (E)
c. Find P (C or D)
d. Find P (A and B)
e. Find P(C/D)
7. (6) The average age of freshman college students is 18.5 years, with a standard
deviation of 0.4 years.
a. Let x? denote the mean age of a random sample of n = 50 students. Determine the mean and standard deviation of the random variable x?.
b. Repeat part (a) with n = 100 students.
8. (6) An insurance company stated that in 1987, the average yearly car insurance cost for a family in the U.S. was $1188. In the same year, a random sample of 37 families in California resulted in a mean cost of $1228 with a standard deviation of $21.00. Does this suggest that the average insurance cost for a family in California in 1987 exceeded the stated national average?
a. State the appropriate hypotheses for this question.
b. Test your hypotheses at a significance level of 5%. Interpret your results.
9. (6) Thirty-five fourth-grade students were asked the traditional question “what do you want to be when you grow up”. The responses are summarized in the following table:
Employment Frequency Relative Frequency
Teacher 8 0.229
Doctor 6 0.171
Scientist 3 0.086
Police Officer 9 0.257
Athlete 9 0.257
a. Construct a pie chart for relative frequencies
b. Construct a bar graph for the relative frequencies
c. Construct a pareto chart and explain the finding
10. (6) The random variable x is the number of houses sold by a realtor in a single month at the real-estate office. Its probability distribution is:
Houses sold (x) Probability P(x)
a. Compute the mean of the random variable.
b. Compute the standard deviation of the random variable.
11. (6) In a college freshman English course, the following 20 grades were recorded
48 88 47 39 45 44 98 76 84 54
67 91 84 38 75 38 35 82 42 82
a. Quartiles for the above data set
b. Range for the above data set
c. Mean for the above data set
d. Variance for the above data set
e. Coefficient of variation for the above data set
12. (6) A brand of salsa comes in jars marked net weight 680 grams. Suppose the actual mean net weight of all jars is 680 grams with a standard deviation of 22.7 grams. Further suppose that the net weights are normally distributed.
a. Determine the probability that a randomly selected jar of this brand of salsa will have a weight less than 660 grams.
b. Determine the probability that 15 randomly selected jars of this brand of salsa will have a mean weight of less than 660 grams.
c. Why are these probabilities not the same?
13. (7) A computerized tutorial center at a local college wants to compare two different statistical software programs. Students going to the center are matched with other student having similar abilities in statistics. A random sample of 10 student pairs is selected. One student is randomly assigned program A, the other program B. After two weeks of using the program, the students are given an evaluation test. Their grades are:
Program A Program B
Do the data provide evidence, at the 10% significance level, that there is a difference in mean student performance between the two software programs?
a) In support of your decision show the hypotheses and the value of the test statistics computed for assessing the significance level.
b) What is the actual type 1 error?
14. (6) A college administrator wants to study the average age of students who drop out of college after attending only one semester. He randomly selects 25 students who are in this group. Their ages are listed below:
35.6 20.1 18.1 21.3 20.1 19.2 18.5 18.9 18.6 18.4 19.2
18.8 17.7 21.0 19.3 24.2 19.0 19.6 18.6 19.4 20.3 20.4
19.6 19.9 19.2
Because the administrator has been doing these studies in the past, he knows that age is normally distributed with a standard deviation of 0.8 years.
a. Find a 95% confidence interval for the mean age of all first semester college dropouts.
b. Interpret your results in part (a) in words.
15. (7) Does smoking have an effect on worker accidents? You have collected some data on accidents and are able to use data from a sample of 34 workers who were involved in an accident last year. You also have data from another sample of 32 workers who were not involved in accidents last year. You ask all the workers in your samples if they smoked last year. You found 16 workers who had accidents were smokers while 6 workers who did not have accidents were smokers.
a) State the hypotheses for this problem and test it.
b) What is the probability of a type 1 error?
16. (6) A survey of 1000 adults was conducted concerning “green practices”. In response to a question of what was the most beneficial thing to do for the environment, 28% said “buying renewable energy”.
a) Predict what percentage of the population of adults would answer this way if they were all asked. You would like to be 95 percent confident you will be correct.
b) Next year you will repeat this study. Determine the sample size necessary to estimate, with 95% confidence, the population percentage to within plus and minus 0.02 or 2%.