2. Exercise 2.25 introduces a study of 678 women who had gone off birth control
ID: 3217222 • Letter: 2
Question
2. Exercise 2.25 introduces a study of 678 women who had gone off birth control with the intention of becoming pregnant. Table B.6 includes information on whether or not a woman was a smoker and whether or not the woman became pregnant during the first cycle. We wish to estimate the difference in the proportion who successfully get pregnant between smokers and non-smokers.
Table B.6
Smoking and pregnancy rate
Smoker
Non-smoker
Total
Pregnant
38
206
244
Not pregnant
97
337
434
Total
135
543
678
(a)
Find the best point estimate for the difference in proportions.
(b)
Use StatKey or other technology to find and interpret a 90% confidence interval for the difference in proportions. Is it plausible that smoking has no effect on pregnancy rate?
3. Exercises B.24 and B.25 describe a study to determine whether a sales tax on soda will reduce consumption of soda in the US below the current per-capita level of about 50 gallons of soda per year. The hypotheses for the test are H0:=50 vs Ha:<50, where represents the average annual consumption of soda in communities where the sales tax is implemented.
(a)
Suppose sample results give a p-value of 0.02. Interpret this p-value in terms of random chance and in the context of taxes and soda consumption.
(b)
Now suppose sample results give a p-value of 0.41. Interpret this p-value in terms of random chance and in the context of taxes and soda consumption.
(c)
Which p-value, 0.02 or 0.41, gives stronger evidence that a sales tax will reduce soda consumption?
(d)
Which p-value, 0.02 or 0.41, is more statistically significant?
4. The Super Bowl is the final championship game in the National Football League in the US, and is one of the most watched television events of the year. In February 2012, just before Super Bowl XLVI, a random sample62 of 1807 American adults were asked if they plan to watch the Super Bowl. A 95% confidence interval for the proportion planning to watch is 0.61 to 0.65.
(a)
What is the population? What is the sample?
(b)
Interpret the confidence interval in context.
(c)
Approximately what is the best point estimate and margin of error for the estimate?
5. Exercise B.33 describes a study on the use of ketamine in treating depression in mice. Ten depressed mice given the drug had a mean score of 135 seconds on a forced-swim test used to measure depression (lower scores indicate less depression). The usual mean for depressed mice on this test is about 160 seconds.
(a)
Using the parameter to denote the mean score on this test for depressed mice after treatment with ketamine, what are the null and alternative hypotheses for seeing if there is evidence that the mean score is lower than 160?
(b)
Describe carefully how to use slips of paper to generate one randomization statistic for this test. In particular, how many slips of paper are needed and what do we write on them? What do we do with them to obtain a randomization sample? What statistic do we then record?
6. The Centers for Disease Control and Prevention (CDC) conducted a randomized trial in South Africa designed to test the effectiveness of an inexpensive wipe to be used during childbirth to prevent infections.65 Half of the mothers were randomly assigned to have their birth canal wiped with a wipe treated with a drug called chlorohexidine before giving birth and the other half to get wiped with a sterile wipe (a placebo). The response variable is whether or not the newborns develop an infection. The CDC hopes to find out whether there is evidence that babies delivered by the women getting the treated wipe are less likely to develop an infection.
(a)
Define the relevant parameter(s) and state the null and alternative hypotheses.
(b)
What is/are the sample statistic(s) to be used to test this claim?
(c)
If the results are statistically significant, what would that imply about the wipes and infections?
(d)
If the results are not statistically significant, what would that imply about the wipes and infections?
7. Is lie detection software accurate? Exercise A.23 describes a study in which 48 individuals read a truthful passage while under stress and while connected to a lie detector. The lie detection software inaccurately reported deception in 57% of the cases. A bootstrap distribution shows an estimated standard error of 0.07.
(a)
Give a point estimate for the population parameter of interest.
(b)
Give a 95% confidence interval for this population parameter.
(c)
Comment on the accuracy of this lie detector. Do you think results from this lie detector should hold up in court?
Smoker
Non-smoker
Total
Pregnant
38
206
244
Not pregnant
97
337
434
Total
135
543
678
Explanation / Answer
Answer:
Question 2 answered.
2. Exercise 2.25 introduces a study of 678 women who had gone off birth control with the intention of becoming pregnant. Table B.6 includes information on whether or not a woman was a smoker and whether or not the woman became pregnant during the first cycle. We wish to estimate the difference in the proportion who successfully get pregnant between smokers and non-smokers.
Table B.6
Smoking and pregnancy rate
Smoker
Non-smoker
Total
Pregnant
38
206
244
Not pregnant
97
337
434
Total
135
543
678
(a)
Find the best point estimate for the difference in proportions.
Group 1
Number of Items of Interest
38
Sample Size
135
Group 2
Number of Items of Interest
206
Sample Size
543
Intermediate Calculations
Group 1 Proportion
0.2815
Group 2 Proportion
0.3794
Difference in Two Proportions
-0.0979
(b)
Use StatKey or other technology to find and interpret a 90% confidence interval for the difference in proportions. Is it plausible that smoking has no effect on pregnancy rate?
Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level
90%
Intermediate Calculations
Z Value
1.645
Std. Error of the Diff. between two Proportions
0.0440
Interval Half Width
0.0723
Confidence Interval
Interval Lower Limit
-0.1702
Interval Upper Limit
-0.0256
90% CI = (-0.1702, -0.0256)
Since 0 value not in the interval, it is plausible that smoking has no effect on pregnancy rate.
Smoker
Non-smoker
Total
Pregnant
38
206
244
Not pregnant
97
337
434
Total
135
543
678
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