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Chapter 8: Q.28 (page 496)

High tuition costs Glenn wonders what proportion of the students at his school think that tuition is too high. He interviews an SRS of 50 of the 2400 students at his college. Thirty-eight of those interviewed think tuition is too high.

Short Answer

Expert verified

All three conditions for confidence interval is satisfied.

Step by step solution

01

Step-1 Given Information

Given in the question that,

Population size=2400

number of sample=50

number of success=38we have to calculate what proportion of the students at his school think that tuition is too high.

02

Step-2 Explanation

Three conditions must be met in order to construct a confidence interval. Random, Independent, and Normal are the conditions.

The requirement of randomness is met because the sample was drawn at random among the college students. The requirement for independence is satisfied because the sample size is less than 10% of the population size. In the study, there are 38success stories and 12failure stories. Because both the success and the success rate are more than ten. As a result, the typical condition is met. As a result, all three confidence interval conditions are met.

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Most popular questions from this chapter

The Gallup Poll interviews 1600people. Of these, 18%say that they jog regularly. The news report adds: "The poll had a margin of error of plus or minus three percentage points at a 95%confidence level." You can safely conclude that

(a) 95%of all Gallup Poll samples like this one give answers within卤3%of the true population value.

(b) the percent of the population who jog is certain to be between 15%and21%.

(c) 95%of the population jog between5%and21%of the time.

(d) we can be 95%confident that the sample proportion is captured by the confidence interval.

(e) if Gallup took many samples,95%of them would find that 18%of the people in the sample jog.

26. Sisters and brothers (3.1, 3.2) How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches)
of 11 adult pairs:

Brother
71
68
66
67
70
71
70
73
72
65
66
Sister
69
64
65
63
65
62
65
64
66
59
62

(a) Construct a scatterplot using brother鈥檚 height as the explanatory variable. Describe what you see.
(b) Use your calculator to compute the least-squares regression line for predicting sister鈥檚 height from brother鈥檚 height. Interpret the slope in context.
(c) Damien is 70 inches tall. Predict the height of his sister Tonya.
(d) Do you expect your prediction in (c) to be very accurate? Give appropriate evidence to support your answer.

You have measured the systolic blood pressure of an SRS of 25company employees. A 95%confidence interval for the mean systolic blood pressure for the employees of this company is (122,138). Which of the following statements gives a valid interpretation of this interval?

(a) 95%of the sample employees have systolic blood pressure between 122and138.

(b) 95%of the population of employees have systolic blood pressure between 122and138.

(c) If the procedure were repeated many times, 95%of the resulting confidence intervals would contain the population mean systolic blood pressure.

(d) The probability that the population mean blood pressure is between 122and138is 0.95.

(e) If the procedure were repeated many times, 95%of the sample means would be between122and138.

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

R8.3. Batteries A company that produces AA batteries tests the lifetime of a random sample of 40 batteries using a special device designed to imitate real-world use. Based on the testing, the company makes the following statement: 鈥淥ur AA batteries last an average of 430 to 470 minutes,
and our confidence in that interval is 95%.
(a) Determine the sample mean and standard deviation.
(b) A reporter translates the statistical announcement into 鈥減lain English鈥� as follows: 鈥淚f you buy one of this company鈥檚 AA batteries, there is a 95% chance that it will last between 430 and 470 minutes.鈥� Comment on this interpretation.
(c) Your friend, who has just started studying statistics, claims that if you select 40 more AA batteries at random from those manufactured by this company, there is a 95% probability that the mean life time will fall between 430 and 470 minutes. Do you agree? Explain.
(d) Give a statistically correct interpretation of the confidence interval that could be published in a newspaper report.
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