1016-320 Data Analysis 2
Review for Test 1
Part II
In each of the following scenarios:

Identify the parameter(s) of interest

Indicate what you would do next to answer the question

If you would calculate a confidence interval, explain how you would use it, and state the conclusion

If you would do test of hypotheses then state the five steps, the appropriate values, and conclusion.
This is your day 11 assignment and it is due today. The solution will be posted by Thursday noon. On Friday, you will be presented with a similar collection of problems (but fewer of them). You will be asked to use Minitab to obtain results and write your conclusions, as you have been doing all quarter.
1. A governor is concerned about his “negatives”: The percentage of state residents who express disapproval of his job performance. His political committee paid for a series of TV ads, hoping that they can keep the negatives below 30%. After the ads have run, a follow-up poll of 1200 residents showed that 345 rated the governor negatively. p = proportion of residents who disapprove of the governor
The directional nature of the question implies that a hypothesis test is called for, though one could construct a confidence interval anyway.
If we do a hypothesis test, we have Ho: p = .3 and Ha: p < .3. (They desire a small P-value so they can reject Ho and conclude the proportion of ‘negatives’ is below 30%.)
We could also construct a confidence interval for π, in which case the committee is hoping to find the CI entirely below .3.
Both the CI and the (directional) test can be performed in Minitab using the 1-Proportion menu with Summarized Data. We usually click the Options button and select to use the normal distribution.
1016-320 Data Analysis II
Day 11
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2. The data below were obtained on the total nitrogen concentration (in parts per million) of water drawn from a lake being considered for use as a source of drinking water.
.042
.048
.045
.023
.023
.035
.052
.045
.049
.048
.049
.038
.036
.043
.028
.035
.045
.044
.025
.026
.025
.055
.039
.059
To be acceptable as a source of drinking water, the mean nitrogen content must lie below .07 ppm. Does this lake appear to meet this criteria?
μ = mean nitrogen concentration
The directional nature of the question implies that a hypothesis test is called for, though one could construct a confidence interval anyway.
Ho: μ = .07 versus
Ha: μ < .07
If a confidence interval is constructed, we would hope to find that the entire CI falls below
.07.
In Minitab, choose 1-Sample t.
3. Among a sample of 150 single women who are heads of households, 73 owned their own home. Among a sample of 125 single men who are heads of households, 51 owned their own homes. Is there a difference, between single men and single women, in their rate of home ownership? p
1
= proportion of single men who own homes p
2
= proportion of single women who own homes
Ho: p
1
= p
2 versus Ha: p
1
≠ p
2
Alternatively, one could construct a CI for the difference p
1
- p
2
. If the interval contains zero, then there is not strong evidence of a difference.
In Minitab, choose 2-Proportions for summarized data. We usually click the Options button and select to use the pooled estimate of p.
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Day 11
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4. Consumer Reports tested 14 brands of vanilla yogurt and found the following numbers of calories per serving:
160 200 220 230 120 180 140
130 170 190 80 120 100 170
A diet guide claims that you will get 120 calories from a serving of vanilla yogurt.
μ = mean calories
Ho: μ = 120 versus
Ha: μ ≠ 120 or construct a confidence interval for μ and see if the value 120 is included.
In Minitab, choose 1-Sample t; the data would be in a column and the hypothesized mean is
120.
5. In 1995, a survey of cigarette smoking was done in an attempt to determine if there was a race based difference in smoking of cigarettes. In the survey, 136 of 550 white adults surveyed reported that they smoked cigarettes, while 142 of the 550 black adults surveyed were smokers. p
1
= proportion of white adults who smoke p
2
= proportion of black adults who smoke
Ho: p
1
= p
2 versus Ha: p
1
≠ p
2
Alternatively, one could construct a CI for the difference p
1
- p
2
. If the interval contains zero, then there is not strong evidence of a difference.
In Minitab, choose 2-Proportions for summarized data; the hypothesized difference is zero.
We usually click the Options button and select to use the pooled estimate of p.
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Day 11
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6. Demographic data for the US is often broken down by Standard Metropolitan Statistical
Areas (SMSA’s). A sample of the rates of reported rapes per 100,000 inhabitants is summarized below for selected SMSA’s from South and North areas of the US. Do these data provide evidence of a difference in the rates of reported rapes?
Area n
 x s
South
North
20 40.8 13.4
25 38.4 21.3
μ
1
= rate of rape in the South area of the U.S.
μ
2
= rate of rape in the North area of the U.S.
The two groups are independently selected.
Ho: μ
1
= μ
2 versus Ha: μ
1
≠ μ
2
Alternatively, one could construct a CI for the difference μ
1
- μ
2
. If the interval contains zero, then there is not strong evidence of a difference.
In Minitab, choose 2-Sample t for Summarized data; the hypothesized mean (difference) is zero. We generally do not assume equal variances.
7. To compare two programs for training workers to perform a skilled job, 20 workers are included in an experiment. Of these, 10 are selected at random to be trained by method 1; the remaining
10 are to be trained by method 2. After completion of training, all the workers are subjected to a time-and-motion test that records the speed of performance of a skilled job. Is one method better than the other?
Time (in minutes)
Method 1 15 20 11 23 16 21 18 16 27 24
Method 2 23 31 13 19 23 17 28 26 25 28
μ
1
= mean time to complete task using method 1
μ
2
= mean time to complete task using method 2
The two groups are independently selected.
Ho: μ
1
= μ
2 versus
Ha: μ
1
≠ μ
2
Alternatively, one could construct a CI for the difference μ
1
- μ
2
. If the interval contains zero, then there is not strong evidence of a difference.
In Minitab, choose 2-Sample t; the data are probably stored in different columns and the hypothesized mean (difference) is zero. We generally do not assume equal variances.
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Day 11
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8. A study is conducted to compare the relative effectiveness of two kinds of cough medicines in increasing sleep. Six people with colds are given medicine A the first night, and medicine B on the second. Their hours of sleep each night are recorded below. Is one medicine better than the other?
Subject 1 2 3 4 5 6
Medicine A 4.8 4.1 5.8 4.9 5.3 7.4
Medicine B 3.9 4.2 5.0 4.9 5.4 7.1
μ
1
= mean hours of sleep using medicine A
μ
2
= mean hours of sleep using medicine B
Ho: μ
1
= μ
2 versus Ha: μ
1
≠ μ
2
The two groups are dependent and so we usually work with the difference
μ d
= μ
1
μ
2
= mean difference in hours sleeping
Ho: μ d
= 0 versus
Ha: μ d
≠ 0
Alternatively, one could construct a CI for the mean difference μ d
. If the interval contains zero, then there is not strong evidence of a difference. In Minitab, choose Paired t; the data would probably be stored in columns.
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Day 11
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