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Chapter 8: Q. 15 (page 483)

The AP Statistics class in Exercise 1 also asked an SRS of 20 boys at their school how many shoes they have. A 95% confidence interval for the difference in the population means (girls 鈥� boys) is 10.9 to 26.5. Interpret the confidence interval and the confidence level.

Short Answer

Expert verified

Interpretation confidence level: The confidence interval contains the true difference in population means, on average, in 95%of all samples.

Step by step solution

01

Given Information

A 95% confidence interval for the difference in the population means (girls 鈥� boys) is 10.9 to26.5.

02

Explanation

The given 95%confidence interval for the difference in population means is 10.9to 26.5.

Interpretation: We are 95%confident that the difference in the population means between girls and boys is between 10.9and 26.5.

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Most popular questions from this chapter

A radio talk show host with a large audience is interested in the proportion pof adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100people who phoned in, 70answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?

I. The data are a random sample from the population of interest.

II. nis so large that both np铃�andn1-p铃�are at least 10.

III. The population is at least 10times as large as the sample.

(a) I only

(c) III only

(c) I, II, and III

(b) II only

(d) I and II only

Power lines and cancer (4.2,4.3)Does living near power lines cause leukemia in children? The

National Cancer Institute spent 5 years and $5million gathering data on this question. The researchers compared 638children who had leukemia with620who did not. They went into the homes and actually measured the magnetic fields in children's bedrooms, in other rooms, and at the front door. They recorded facts about power lines near the family home and also near the mother's residence when she was pregnant. Result: no connection between leukemia and exposure to magnetic fields of the kind produced by power lines was found.

(a) Was this an observational study or an experiment? Justify your answer.

(b) Does this study show that living near power lines doesn't cause cancer? Explain.

Hallux abducto valgus (call it HAV) is a deformation of the big toe that is fairly uncommon in youth and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in a random sample of patients under the age of 21who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. For these 21patients, the mean HAV angle was 24.76degrees and the standard deviation was 6.34degrees. A dot plot of the data revealed no outliers or strong skewness.

(a) Construct and interpret a 90%confidence interval for the mean HAV angle in the population of all such patients.

(b) Researchers omitted one patient with an HAV angle of 50degrees from the analysis due to a measurement issue. What effect would including this outlier have on the confidence interval in (a)? Justify your answer.

Going to the prom Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom

Auto emissions Refer to Exercise 6. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals? (Use Figure 8.5, on page 474, as a model for your drawing.)
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