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Chapter 8: Q. T8.5 (page 549)

You want to compute a 90%confidence interval for the mean of a population with an unknown population standard deviation. The sample size is 30. What critical value should you use for this interval?

a. 1.645

b. 1.699

c. 1.697

d. 1.96

e. 2.045

Short Answer

Expert verified

The critical value that should be used in this interval is1.699

The required correct option is (b)

Step by step solution

01

Given information

The standard deviation of the population is unknown.

Sample size (n)=30

Confidence level =90%

02

The objective is to find out the critical value that should be used in this interval

The level of significance is:

Level of significance (伪)=1-Confidence level

=1-0.90=0.10

The t-critical value must be calculated here.

The degree of freedom is calculated as follows:

localid="1654412235779" (df)=n-1=30-1=29

The critical value at 29degrees of freedom and a 10%significance level is calculated as follows:

t伪2,df=t0.102,29=1.699

Therefore, the correct option is(b)

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Most popular questions from this chapter

More cheating Refer to Exercise 36. Calculate and interpret the standard error of p^for these data.

Batteries A company that produces AA batteries tests the lifetime of a randomsample of 30 batteries using a special device designed to imitate real-world use. Based onthe 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%.鈥�36

a. Determine the point estimate, margin of error, standard error, and sample standard

deviation.

b. A reporter translates the statistical announcement into 鈥減lain English鈥� as follows: 鈥�95% of this company鈥檚 AA batteries last between 430 and 470 minutes.鈥� Comment on this interpretation.

c. Your friend, who has just started studying statistics, claims that there is a 95% probability that the mean lifetime will fall between 430 and 470 minutes. Do you agree? Explain your reasoning.

d. Give a statistically correct interpretation of the confidence level that could be published in a newspaper report.

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

a. How much time do students at your school spend on the Internet? You collect data from the 32members of your AP Statistics class and calculate the mean amount of time that these students spent on the Internet yesterday.

b. Is the real-estate market heating up? To estimate the mean sales price, a realtor in a large city randomly selected 100home sales from the previous 6months in her city. These sales prices are displayed in the boxplot.

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95%confidence and a margin of error no greater than 0.03. How large a random sample do we need?

Gambling and the NCAA Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student athletes concerning their gambling-related behaviors. Of the 5594Division Imale athletes who responded to the survey, 3547reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities. A report of this study cited a 1%margin of error.

a. The confidence level was not stated in the report. Use what you have learned to

estimate the confidence level, assuming that the NCAA took an SRS.

b. The study was designed to protect the anonymity of the student athletes who responded. As a result, it was not possible to calculate the number of students who were asked to respond but did not. How does this fact affect the way that you interpret the results?
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