1. Based on a sample of 50 x-values having mean 35.36 and standard deviation 4.26,
(a) Test at the 0.05 level of significance the null hypothesis : m = 34 versus the alternative : m¹ 34.
(b) find a 95% confidence interval for the population mean.
(c) determine if the results to part (a) and (b) are mutually consistent.
(d) use Minitab to give the p-value for the test in (a).
.2. The data set CHS\NBA.MTP contains a number of variables for guards in the National Basketball Association.
(a) For the variable PPG, meaning points per game, test the null hypothesis mPPG = 11 against the alternative mPPG¹ 11 using the 0.05 level of significance. The data file has n = 105, = 10.70, s= 6.058.
(b)Find a 95% confidence interval for mPPG and reconcile your conclusion in (a) with this interval.
3. Suppose that a sample of 200 accounts receivable entries at a large mail-order business had a mean price of $846.20 and a standard deviation of $1,840.80. Give a 95% confidence interval for the population mean. Be sure to state any assumptions that you use.
5. Suppose that you are asked to test H0: m1 = m2 versus H1: m1¹m2 based on these data:
|
Sample
|
n
|
Average
|
St.Dev.
|
|
1
|
27
|
-0.0491
|
0.0990
|
|
2
|
23
|
-0.0307
|
0.0496
|
Which form of the test would you use? What conclusion would you reach? The next problem asks for additional calculations with the same numbers.
6. The weekly salaries of union electricians in two metropolitan areas were compared by taking random samples of 50 in each area. The results were these:
|
Area
|
N
|
Mean
|
Standard deviation
|
|
1
|
50
|
612.26
|
100.20
|
|
2
|
50
|
659.65
|
83.73
|
At the 5% level of significance, test the hypothesis : m1 = m2 versus the alternative : m1≠m2 .
7. The management at Jackson & Flinch brokerage services has established dollar quotas for each of their brokers, but the brokers are generally not informed about these quotas. As part of an experiment, 21 brokers (selected at random) were actually told their annual dollar quotas - just to see how knowledge of the quota would influence their performance. These brokers were compared with 15 others who were not told their quotas. The data below indicate the fraction of annual quotas achieved by the end of October:
|
Told about quota?
|
N
|
Mean
|
Standard deviation
|
|
No
|
15
|
0.8710
|
0.0598
|
|
Yes
|
21
|
0.8924
|
0.0638
|
At the 0.05 level of significance, test the null hypothesis : mNO = mYES against the alternative : mNO¹mYES.
8. The distributor of a certain variety of tomato seed has promised that 80% of the seeds will germinate under standard greenhouse conditions. You test this claim with 500 seeds, and you find that 362 germinate successfully. At the 5% level of significance, test the claim as H0: p = 0.80 against the alternative H1: p ¹ 0.80.
9. Employees at McKenzie Corporation were given the opportunity to start 401-K retirement plans beginning January 1, 2002, and 196 employees chose to do so. Of these, there were 94 who elected to sit through a three-hour seminar on making investment decisions. The dollar values of all these employees were noted on December 31, 2004, exactly two years later:
|
Attend seminar?
|
n
|
Mean
|
Standard deviation
|
|
No
|
102
|
10,900
|
1,440
|
|
Yes
|
94
|
11,500
|
3,570
|
At the 0.05 level of significance, test the null hypothesis : mNO = mYES against the alternative : mNOYES.
10. As part of an investigative process, a financial reporter has been comparing the advice given by two investment newsletters. Each time a "buy" recommendation was given, he noted the stock price; he then recorded whether the price was higher in exactly three months. Each case in which the price was higher was called a "success." Here is the summary of his findings:
|
Newsletter
|
Success
|
Failure
|
Total number
of "buy" recommendations
|
|
Third Millenium
|
28
|
15
|
43
|
|
Global Starship
|
44
|
36
|
80
|
Based on these values, does the reporter have an interesting story?
11. People on marketing panels are often given products to use at home and evaluate. In one panel, 75 people were given a one-gallon jug of Sunshine Cal-Plus Orange Juice to take home, and another 80 people were given a one-gallon jug of CitriSplash Orange Juice to take home. When the panelists returned exactly one week later they were asked, "Did you finish the gallon of orange juice?" Here are the responses:
|
Juice Brand
|
Finished Juice
|
Did Not Finish Juice
|
Total
|
|
Sunshine
|
32
|
43
|
75
|
|
CitriSplash
|
54
|
26
|
80
|
|
Total
|
86
|
69
|
155
|
At the 0.05 level of significance, is there a difference between these two juices for this particular question?