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Chapter 8: Q 71. (page 542)

America’s favorite cookie Ann and Tori wanted to estimate the average weight of an Oreo cookie to determine if it was less than advertised (34 grams for 3 cookies). They selected a random sample of 36cookies and found the weight of each cookie (in grams). The mean weight was x̄=11.3921grams with a standard deviation of sX=0.0817grams. Construct and interpret a 90%confidence interval for the true mean weight of an Oreo cookie.

Short Answer

Expert verified

The confidence interval is(11.37,11.42).

Step by step solution

01

Given Information

It is given that (x¯)=11.3921

sx=0.0817

n=36

02

Concept Used

tconfidence interval for population mean is calculated as:

CI=x¯±tα/2,df×sn

03

Calculation

As standard deviation is not known, tconfidence interval is used.

Excel gives output as:

Confidence Interval is(11.37,11.42)

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Most popular questions from this chapter

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?

Prayer in school Refer to Exercise 5.

a. Explain what would happen to the length of the interval if the confidence level were increased to 99%.

b. How would a 95%confidence interval based on double the sample size compare to the original 95%interval?

c. The news article goes on to say: “The theoretical errors do not take into account

additional errors resulting from the various practical difficulties in taking any survey of public opinion.” List some of the “practical difficulties” that may cause errors which are not included in the ±3 percentage point margin of error.

Weeds among the corn Velvetleaf is a particularly annoying weed in cornfields. It produces lots of seeds, and the seeds wait in the soil for years until conditions are right for sprouting. How many seeds do velvetleaf plants produce? The histogram shows the counts from a random sample of 28plants that came up in a cornfield

when no herbicide was used. Determine if the Normal/Large Sample condition is met in this context.

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.

Good wood? A lab supply company sells pieces of Douglas fir 4 inches long and

1.5 inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a distribution with standard deviation 3000 pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000 pounds with 95% confidence. How large a sample is needed?
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