Remember what we went over in class concerning showing all your work on the excel sheet, no cut and paste and no answers on MS -Word.
This assignment will be turned in an excel spreadsheet. You must show all work. If you cut and paste I will give you no credit for it. If it comes in in any format except EXCEL I will not grade it and you will get a zero for your final score. I will not accept any posting coming in after the due date.
1. Classify the following studies as descriptive or inferential and explain your reasons:
a. (1 pts.) 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. (1 pts.) A report in a farming magazine indicates that more than 95% of the 400 largest farms in the nation are still considered family operations.
2. 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. (2 pts.) Construct a pie chart for relative frequency
b. (2 pts.) Construct a bar graph for the relative frequencies
3. 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
Find the:
a. (1 pt.)Quartiles for the above data set
b. (1 pt.)Range for the above data set
c. (1 pt.)Mean for the above data set
d. (1 pt.)Variance for the above data set
4. 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
30 – 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 under 35
a. (2 pts.) Find P (B)
b. (2 pts.) Find P (E)
5. 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 is
a. (2 pts.) satisfied with job
b. (3 pts.) did not attend college
given
not satisfied with the job
c. (3 pts.) not satisfied with job, and did not attend college
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)
0
0.09
1
0.24
2
0.21
3
0.17
4
0.03
5
0.15
6
0.09
7
0.02
a. (3 pts.) Compute the mean of the random variable.
b. (3 pts.) Compute the standard deviation of the random variable.
7. 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. (1 pt.) About 68.26% of 18 -24 year old American males are between ______ and ______ inches tall.
b. (1pt.) About 95.44% of 18 -24 year old American males are between ______ and ______ inches tall.
c. (1 pt.) About 99.74% of 18 -24 year old American males are between ______ and ______ inches tall.
8. The average of freshman college students is = 18.5 years, with a standard
deviation = 0.4 years.
a. (4 pts.) Let x̅ denote the mean age of a random sample of n = 50 students. Determine the mean and standard deviation of the random variable x̅.
b. (4 pts.) Repeat part (a) with n = 100.
9. A brand of salsa comes in jars marked net weight 680 grams. Suppose the actual mean net weight μ = 680 grams with a standard deviation of 22.7 grams. Further suppose that the net weights are normally distributed.
a. (4 pts.) Determine the probability that a randomly selected jar of this brand of salsa will have a weight less than 660 grams.
b. (4 pts.) Determine the probability that the 15 randomly selected jars of this brand of salsa will have a mean weight of less than 660 grams.
(8 pts.) 10. 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 stating monthly salary of x̅ = $1635 with a standard deviation of s = $288. Use these data to obtain a 90% confidence interval estimate for the mean starting monthly salary, µ, of all recent graduates with bachelor’s degrees in marketing from this university.
11. A college administrator wants to study the average age of students who drop out of college after only attending 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
Assume that the ages are normally distributed with a standard deviation of sigma = 0.8 year.
a. (5 pts.) Find a 95% confidence interval for the mean age, µ, of first semester college dropouts.
b. (3 pts.) Interpret your results in part (a) in words.
12. 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 x̅ = $1228 with a standard deviation of s = $21.00.
a. (4 pts.) Does this suggest that the average insurance cost for a family in California in 1987 exceeded the national average?
b. (4 pts.) State the appropriate null and alternative hypotheses for this question.
c. (4 pts.) Perform the statistical test of the null hypothesis at a significance level of 5%
(10 pts.) 13. 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 (assume the matching process creates matched pairs acceptable for use with the appropriate paired test statistic for the null hypothesis of no difference). A random sample of 10 student pairs is selected for each pair, 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
64
62
68
72
75
79
97
57
90
91
55
56
68
88
64
89
91
77
95
76
Do the data provide evidence, at the 5% significance level, that there is a difference in mean student performance between the two software programs? Assume that the population of all possible paired differences is approximately normally distributed. In support of your decision show the null and alternative hypothesis and the value of the test statistics computed for assessing the significance level.
14. 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 versus their current GPAs:
Entering GPA
Current GPA
3.5
3.5
3.8
3.6
3.9
3.5
3.7
3.9
4.0
3.5
4.0
3.7
3.6
3.6
3.9
3.6
3.7
4.0
4.0
3.9
a. (3 pts.) Determine the linear regression equation for the data.
b. (3 pts.) Graph the regression equation
c. (3 pts.) Describe the apparent relationship between the entering GPAs and current GPAs for students in this graduate program.
d. (3 pts.) What does the slope for the regression line represent in terms of current GPAs?
e. (3 pts.) Use the regression equation to predict the current GPA of a student with an entering GPA of 3.6
