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Chapter 8: Q.67 (page 481)

Construct a 95% confidence interval for the population proportion of households where the women make the majority of the purchasing decisions. State the confidence interval, sketch the graph and calculate the error bound.

Short Answer

Expert verified

The confidence interval: CI:(0.532,0.668)

Margin of error =0.0679

Step by step solution

01

Given Information

A 95%confidence interval for the population proportion of households.

02

Explanation

Here we need to find the margin of errors,

That are,

Margin Of Error=Z伪2脳p鈥�1鈭�p鈥�n

=Z0.052脳1202001鈭�120200200

=[1.96脳0.03464]

=0.0679

Now we need to find the confidence interval

Confidence Interval=p鈥�卤Za2脳p(1鈭�p)n

=120200卤Z0.052脳1202001鈭�120200200

=120200卤1.96脳0.03464

=[0.532,0.668]

The confidence interval is CI:(0.532,0.668).

The graph:

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Most popular questions from this chapter

Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8;8;10;7;9;9. Assume the underlying distribution is approximately normal.

a. Construct a 90%confidence interval for the population mean grams of fat per serving of chocolate chip cookies

sold in supermarkets.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

b. If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?

c. Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies.

d. Calculate the mean.

e. Is the mean within the interval you calculated in part a? Did you expect it to be? Why or why not?

In one complete sentence, explain what the interval means.

On May 23,2013, Gallup reported that of the 1005people surveyed, 76%of U.S. workers believe that they will continue working past retirement age. The confidence level for this study was reported at 95%with a 卤3%margin of error.

a. Determine the estimated proportion from the sample.

b. Determine the sample size.

c. Identify CL and .

d. Calculate the error bound based on the information provided.

e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between the values.

f. Create a confidence interval for the results of this study.

g. A reporter is covering the release of this study for a local news station. How should she explain the confidence interval to her audience?

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Define the random variable X in words

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a.i.x虅=__________ii.sx=__________iii.n=__________iv.n鈥�1=__________

b. Define the random variables XandX虅in words.

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e. Explain in a complete sentence what the confidence interval means.
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