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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 8: Q 60. (page 524)

More Oranges:The gardener in the previous exercise randomly selects $20$
mandarin oranges from the tree and counts the number of seeds in each orange. Here are the data:
a. Graph the data using a dot plot.
b. Based on your graph, is it plausible that the number of seeds from oranges on this tree follows a distribution that is approximately Normal? Explain your answer.

Short Answer

Expert verified

a.

b. It can't be said that the number of seeds from oranges on this tree follows a distribution that is approximately normal.

Step by step solution

01

Given Information

The count of number of seeds of twenty oranges is given.

02

Dot Plot

Based on given data, dot plot is as below:

03

Deduction from Dot Plot Graph

It can be observed that data points are not falling in center. They lie in right tailed of plot.

Hence, we cannot say that number of seeds from oranges on this tree follows a distribution that is approximately normal.

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Most popular questions from this chapter

Prayer in school A New York Times/CBS News Poll asked a random sample of U.S. adults the question “Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” Based on this poll, the $95 %$ confidence interval for the population proportion who favor such an amendment is $(0.63, 0.69)$ .

a. Interpret the confidence interval.

b. What is the point estimate that was used to create the interval? What is the margin of error?

c. Based on this poll, a reporter claims that more than two-thirds of U.S. adults favor such an amendment. Use the confidence interval to evaluate this claim.

More weight loss Refer to Exercise $6$ . Interpret the confidence level.

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 $330$ goldfish 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.

Explaining confidence The admissions director for a university found that $(107.8, 116.2)$ is a $95 %$ confidence interval for the mean IQ score of all freshmen. Discuss whether each of the following explanations is correct, based on that information.

a. There is a $95 %$ probability that the interval from role="math" localid="1654200953396" $107.8 to 116.2$ contains $μ$ .

b. There is a $95 %$ chance that the interval $(107.8, 116.2)$ contains $\bar{x}$ .

c. This interval was constructed using a method that produces intervals that capture the true mean in $95 %$ of all possible samples.

d. If we take many samples, about $95 %$ of them will contain the interval $(107.8, 116.2)$ .

e. The probability that the interval $(107.8, 116.2)$ captures $μ$ is either $0$ or $1$ , but we don’t know which.

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?

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