Assignments must have a cover page (refer to the course outline). Please write on one side of the page only and show ALL your work. Answer questions with sentences. Include any printout for a question with the question and clearly label the printout with the question number and part. Keep three decimal places.
1) AT&T would like to test the hypothesis that the average revenue per retail user for Verizon Wireless customers equals $50. A random sample of 32 Verizon Wireless customers provided an average revenue of $54.70. It is believed that the population standard deviation for the revenue per retail user is $11.00. AT&T would like to set α = 0.05. Use the critical value approach to test this hypothesis.
2) Hallmark would like to test the hypothesis that those celebrating Valentine's Day will spend more than an average of $125 on gifts. A random sample of 18 people celebrating Valentine's Day spent an average of $148.50 with a standard deviation of $34.90. Hallmark would like to set α = 0.01. Use the p-value approach to test this hypothesis.
3) Hotels.com would like to test the hypothesis that the proportion of American travelers in Europe that prefer an American-branded hotel equals 0.42. A random sample of 90 Americans found that 49 preferred American-branded hotels. Hotels.com would like to set α = 0.05. Use the critical value approach to test this hypothesis.
4) A professor would like to test the hypothesis that the average grade for a student taking a 10 am statistics class averages five points higher than the average grade from a student in an 8 am statistics class. The following data shows the sample size and average grades for students in the two class times along with the population standard deviations.
|
|
10 am
|
8 am
|
|
Sample mean
|
87.1
|
81.4
|
|
Sample size
|
32
|
30
|
|
Population standard deviation
|
3.4
|
3.2
|
Define Population 1 is defined as the 10 am class and Population 2 the 8 am class. Construct an 80% confidence interval for the difference in population mean and interpret the results.
5) Traveler's Insurance would like to test the hypothesis that the average number of miles driven per month by a male teenage driver exceeds the average number of miles driven per month by a female teenage driver by more than 50 miles. The following data summarizes the sample statistics for the miles driven per month by each gender. Assume that the population variances are equal.
|
|
Male
|
Female
|
|
Sample mean
|
685
|
580
|
|
Sample size
|
13
|
16
|
|
Sample standard deviation
|
130
|
120
|
Define Population 1 as male drivers and Population 2 as female drivers and use the critical value approach to test this hypothesis with α = 0.05.
6) American Greetings would like to test the hypothesis that the average amount of money spent per person on Mother's Day increased by more than $10 this year when compared to last year. The following data represents the amount of money that the same eight individuals spent on Mother's Day during the past two holidays.
|
Person
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
Last Year
|
$140
|
$113
|
$86
|
$147
|
$140
|
$162
|
$150
|
$142
|
|
This Year
|
$133
|
$110
|
$156
|
$170
|
$160
|
$166
|
$183
|
$154
|
Define Population 1 as this year and Population 2 as last year and use the p-value approach to test this hypothesis with α = 0.05.
7) John is the manager at the Deerfield Golf Course and would like to test the hypothesis that the average golf score at his course is different from the average golf score at the Pike Creek Golf Course, which is a competitor in the area. The following data represents the golf scores for seven golfers who recently played at both courses.
|
Golfer
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
Deerfield
|
85
|
93
|
96
|
83
|
78
|
80
|
80
|
|
Pike Creek
|
88
|
91
|
99
|
94
|
82
|
85
|
91
|
Define Population 1 as the Deerfield course and Population 2 as the Pike Creek course. Construct a 95% confidence interval for the difference in population mean and interpret the results.
8) The Marseille Water Taxi ferries tourists from the harbor at Marseille, France, to the Frioul Islands in the Mediterranean Sea. The table below shows the number of passengers on the noontime ferry over seven randomly selected days along with the current ambient temperature in degrees Celsius.
|
Temperature
|
Passengers
|
|
16
|
15
|
|
19
|
20
|
|
22
|
20
|
|
26
|
22
|
|
18
|
10
|
|
24
|
18
|
Use the Marseille Water Taxi data to:
A) Describe the regression line that will predict the number of passengers on the noontime ferry based on the ambient temperature.
B) Interpret the slope of the regression equation.
C) Predict number of passengers on the noontime ferry on a day that the ambient temperature is 19 degrees Celsius.
9) The table below shows the number of interceptions thrown during the season by seven randomly selected National Football League teams and the number of games those teams won during the season.
|
Wins
|
Interceptions
|
|
3
|
28
|
|
6
|
19
|
|
11
|
16
|
|
14
|
6
|
|
10
|
9
|
|
8
|
25
|
|
8
|
11
|
Use the NFL team data to calculate:
A) The standard error of the estimate.
B) The 95% confidence interval for the average number of wins for a team that throws 14 interceptions during the season.
10) A manufacturer of flash drives for data storage operates a production facility that runs on three 8-hour shifts per day. The following contingency table shows the number of flash drives that were defective and not defective from each shift.
|
Shift
|
Defective
|
Not Defective
|
|
7AM-3PM
|
7
|
113
|
|
3PM-11PM
|
10
|
90
|
|
11PM-7AM
|
4
|
76
|
Perform a hypothesis test to determine if the quality of the flash drive production and the production shift are independent variables using α = 0.05.