Example 1
The MacBurger Restaurant chain claims that the mean waiting time for customers is 3 minutes with a population standard deviation of 1 minute. The quality assurance department found in a sample of 50 customers at the Gombak branch that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is 3 minutes?
Example 2
The MacBurger Restaurant chain claims that the mean waiting time for customers is 3 minutes with a population standard deviation of 1 minute. The quality assurance department found in a sample of 50 customers at the Gombak branch that the mean waiting time was 2.75 minutes. At the 5 percent significance level, can we conclude that the mean waiting time is less than 3 minutes?
Example 3
Find the -value for both Examples 1 and 2 above. Interpret your -values.
Example 4
The management of White Industries is considering a new method of assembling its gold cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts using the new method was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the 10 percent level of significance, can we conclude that the assembly time using the new method is faster? Also find the -value.
Example 5
Employees in a large company are entitled to 15-minute coffee breaks. A random sample of the duration of coffee breaks for 10 employees was taken with the times shown as: 12, 16, 14, 18, 21, 17, 19, 15, 18, and 16. Assuming that the times are normally distributed, is there enough evidence at the 5% significance level to indicate that, on average, employees are taking longer coffee breaks than they are entitled to? What is the -value?
Example 6
A teacher has just taken a course in statistics and decides to put her new knowledge to work. During the last ten years she has collected the final grades of her classes and found the mean to be 73.6 with a standard deviation of 9. The final grades for this year’s class are as follows:
95 97 84 64 72 88 92 61 76 74 84 85 89 75 76 64 61 72 63 74
The teacher wishes to know if she should consider this year’s final grades as significantly different than previous years. What would her decision be, and why? Use the .05 level of significance. Find the -value.
Example 7
As part of a study of corporate employees, the top management of IIUM wants to compare the distance travelled to work by employees at its branches at Gombak with the distance for those in Kuantan. A sample of 35 Gombak employees showed that they travel a mean of 370 km per month. A sample of 40 Kuantan employees showed that they travel a mean of 380 km per month. The population standard deviation for the Gombak and Kuantan employees are 30 and 26 km, respectively. At the .05 significance level, is there a difference in the mean number of kilometers travelled per month between Gombak and Kuantan employees?
Example 8
Mary Fitzpatrick is the VP for Nursing Services at St Luke’s Memorial Hospital. Recently she noticed in the job postings for nurses that those that are unionized seem to offer higher wages. She decided to investigate and gathered the following information:
Group
Mean wage
Population S.D
Sample size
Union
$ 20.75
$2.25
40
No union
$19.80
$1.90
45
a. Would it be reasonable for her to conclude that union nurses earn more? Use the 0.02 significance level.
b. What is the -value? Interpret it.
Example 9
A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching TV among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching TV was 48.4 minutes with a standard deviation of 18.1 minutes. At the .01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 15 single-earner and 12 dual-earner couples studied.
Example 10
As the regional sales manager for ABC Foods, you are interested to compare the sales volume of ABC Cola when the soft drink is displayed in the normal shelves as compared to an end-aisle promotional display. To test the effectiveness of the end-aisle displays, you select 20 stores from the ABC Foods supermarket chains that all experience similar storewide sales volumes. You then randomly assigned 10 of the 20 stores to place the ABC Cola in the normal shelves while the other 10 stores use the end-aisle promotional display. At the end of one week, the sales of ABC Cola are recorded, as follows:
Display Location
Normal
End-Aisle
22
34
52
62
30
52
71
76
54
67
40
64
84
56
59
83
66
90
77
84
Are the mean weekly sales of ABC Cola the same when using a normal shelf location and when using an end-aisle display? Test at the .05 significance level. Be sure to show all the steps. Also find the -value.
Example 11
To investigate the effectiveness of a training program on customer relations, the organizer had given a pre-training and a post-training survey to the participants. To compare the differences, they computed a post-training survey score and a pre-training survey score. Seven customers were randomly selected and completed both surveys. The survey scores for all the seven customers are shown below:
Customer
Pre-training Survey
Post-training Survey
A
6
8
B
5
5
C
10
10
D
7
10
E
6
8
F
5
6
G
2
8
Test whether the training program was effective in improving customer relations at the .05 significance level.
Example 12
The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas yielded the following results
Number of crimes by area
A
B
C
D
E
F
G
H
Before
14
7
4
5
17
12
8
9
After
2
7
3
6
8
13
3
5
Has there been a decrease in the number of crimes since the launch of the program? Use the 0.01 significance level.
Example 13
At a manufacturing company, workers can use two different methods to perform a production task. To maximize output, the company wants to identify the method with the quickest completion time. A random sample of six workers is used. The data on completion times for the six workers are given below:
Completion Time (minutes)
Worker
Method 1
Method 2
Ali
6.0
5.4
Badar
5.0
5.2
Chin
7.0
6.5
David
6.2
5.9
Eric
6.0
6.0
Fahmi
6.4
5.8
Using .05 level of significance, test that the average completion times differ with one another. What is the -value?
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