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Chapter 8: Q 76. (page 542)

A school of fish Refer to Exercise 74.

a. Explain why it was necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.

b. According to the packaging, there are supposed to be 330goldfish in each bag of crackers. Based on the interval, is there convincing evidence that the average number of goldfish is less than 330? Explain your answer.

Short Answer

Expert verified

a. This because sample size is small.

b. No evidence is present that average number of goldfish is less than330

Step by step solution

01

Given Information

Given data is:317,330,325,323,332,337,324,342,330,349,335,330

02

Necessity of inspecting graph

Sample data consists of 12<30values. To make sure that normal/large condition is satisfied, inspecting graph of sample data is important.

03

Checking if there is evidence that average goldfish is <330

Output using excel is:

Required confidence interval is 325.596<μ<336.738.

The upper limit is higher than 330.

There is no evidence that average goldfish is less than330

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Most popular questions from this chapter

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of \(2. Based on last year’s book sales, we estimate that the standard deviation of the amount spent will be close to \)30. The number of observations required is closest to

(a) 25. (b) 30. (c) 608. (d) 609. (e) 865.

Critical values What critical value t*from Table B should be used for a confidence interval for the population mean in each of the following situations?

a. A 90% confidence interval based on n=12 randomly selected observations

b. A 95% confidence interval from an SRS of 30 observations

c. A 99% confidence interval based on a random sample of size 58

Running red lights A random digit dialing telephone survey of 880 drivers asked, “Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?” Of the 880 respondents, 171 admitted that at least one light had been red.37

a. Construct and interpret a 95% confidence interval for the population proportion.

b. Nonresponse is a practical problem for this survey—only 21.6% of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: Do you think more or fewer than 171 of the 880 respondents really ran a red light? Why? Are these sources of bias included in the margin of error?

Going to the prom Tonya wants to estimate the proportion of seniors in her school who plan to attend the prom. She interviews an SRS of 20of the 750seniors in her school and finds that 36plan to go to the prom.

After deciding on a 95% confidence level, the researcher is deciding between a sample of size n=500 and a sample of size n=1000. Compared with using a sample size of n=500, a confidence interval based on a sample size of n=1000 will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. narrower and would have the same risk of being incorrect.
See all solutions

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