The median age at first marriage in 2010 for women was 26.1 years the highest it has ever been. A random sample of women’s ages (in years) from recently applied for marriage licenses resulted in the following set of ages. At, is there sufficient evidence that the median is not 26.1 years? 34.6, 31.2, 28.9, 28.4, 24.3, 29.8, 25.9, 21.4, 25.1, 26.2, 28.3, 30.6, 35.6, 34.2, 34.1.
- The
median age at first marriage in 2010 for women was 26.1 years the highest it has ever been. A random sample of women’s ages (in years) from recently applied for marriage licenses resulted in the following set of ages. At, is there sufficient evidence that the median is not 26.1 years?
34.6, 31.2, 28.9, 28.4, 24.3, 29.8, 25.9, 21.4, 25.1, 26.2, 28.3, 30.6, 35.6, 34.2, 34.1.
- A study was conducted to see whether a certain diet medication had an effect on the weights (in pounds) of eight randomly selected women. Their weights were taken before and six weeks after daily administration of the medication. The data are shown here. At, can you conclude that the median medication had an effect (increase or decrease) on the weights of the women?
|
Subject |
A |
B |
C |
D |
E |
F |
G |
H |
|
Weight before |
187 |
163 |
201 |
158 |
139 |
143 |
198 |
154 |
|
Weight after |
178 |
162 |
188 |
156 |
133 |
150 |
175 |
150 |
- A researcher wishes to compare the prices for randomly selected prescription drugs in the United States with those in Canada. The same drugs and dosages were compared in each country. At, can it be concluded that the drugs in Canada are cheaper? Using nonparametric test.
|
Drug |
1 |
2 |
3 |
4 |
5 |
6 |
|
United States |
3.31 |
2.27 |
2.54 |
3.13 |
23.40 |
3.16 |
|
Canada |
1.47 |
1.07 |
1.34 |
1.34 |
21.44 |
1.47 |
- Volunteers were randomly assigned to one of two groups to test the speed with which a pain reliever brought relief. One group took the standard dose of extra-strength acetaminophen (group A) while the other group (group N) took a newly approved pain relieving drug. The number of minutes until symptoms abated is listed for each member of each group. At, can it be concluded that there is a difference in the median time until pain is relieved?
|
Group A |
15 |
20 |
12 |
20 |
17 |
14 |
15 |
17 |
18 |
11 |
|
Group N |
7 |
14 |
13 |
11 |
10 |
16 |
12 |
9 |
10 |
9 |
- 5. Random samples of four different cereals show the following numbers of calories for the suggested serving size of each brand. At, is there a difference in the median number of calories for the different brands?
|
Brand A |
112 |
120 |
135 |
125 |
108 |
121 |
|
Brand B |
110 |
118 |
123 |
128 |
102 |
101 |
|
Brand C |
109 |
116 |
125 |
130 |
128 |
132 |
|
Brand D |
106 |
122 |
130 |
117 |
116 |
114 |
- Listed below are the daily numbers (daytime drawing) for the Ghana National Lottery for February 2007. Using O for odd and E for even numbers respectively, test for randomness at.
270, 054, 373, 204, 908, 121, 121, 804, 116, 467, 357, 926, 626, 247, 783, 554, 406, 272, 508, 764, 890, 441, 964, 606, 568, 039, 370, 583.
- Find the rank
correlation coefficient for the following data, which represent the number of hospitals and nursing homes in each of seven randomly selected states. At the 0.05 level of significance, is there enough evidence to conclude that there is a correlation between the two?
|
Hospitals |
107 |
61 |
202 |
133 |
145 |
117 |
108 |
|
Nursing homes |
230 |
134 |
704 |
376 |
431 |
538 |
373 |
- Listed are the numbers of on-demand movies rented per month for 20 customers of a particular cable service. Test the data for randomness at the 0.05 level of significance. What would have to occur to effect the opposite result? Discuss how the data would have to change.
0, 2, 14, 20, 13, 6, 1, 20, 4, 8, 2, 5, 17, 7, 12, 12, 1, 0, 0, 14.
- A marmalade manufacturer produces thousands of jars of marmalade each week. The mass of marmalade in a jar is an observation from a
normal distribution having mean of 455 g and standard deviation 0.8 g.
Following a slight adjustment to the filling machine, a random sample of 10 jars is found to contain the following masses, in grams, of marmalade:
454.8, 453.8, 455.0, 454.4, 455.4, 454.4, 454.4, 455.0, 453.6
Assuming that the variance of the distribution is unaltered by the adjustment, test at the 2% significance level the hypothesis that there has been no change in the mean of the distribution.
- The performances of trainee actors who have passed through a drama school are rated by a panel of experienced actors who assign an overall mark for each trainee. The drama school has recently introduced a new training method which, it is claimed, will lead to better performances.
The marks for a random sample of 6 trainees using the old training method were:
243, 228, 220, 206, 230, 198.
Also the marks of a random sample of 8 using the new method were:
235, 259, 227, 242, 238, 253, 221, 217.
Is there evidence that the new method has led, on average, to higher scores at 1% level of significance?
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