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Chapter 7: Q10 (page 311)

Formats of Confidence Intervals.

In Exercises 9鈥�12, express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red, orange, yellow, and blue M&Ms in Data Set 27 鈥淢&M Weights鈥� in Appendix B.)

Orange M&Ms Express 0.179 < p < 0.321 in the form of p^卤E.

Short Answer

Expert verified

The confidence interval of the format p^卤Eis0.25卤0.071.

Step by step solution

01

Given information

The confidence interval for p is0.179<p<0.321

02

Find the value of sample proportion

Formula for sample proportion is:

p^=upper confidence limit+lower confidence limit2

From the given confidence interval, thelower confidence limit is 0.179 and upper confidence limit is 0.321.

Substituting values,

p^=0.321+0.1792=0.25

Hence, the sample proportion is 0.25.

03

Find the value of margin of error

Formula for margin of error is:

E=upper confidence limit-lower confidence limit2=0.321-0.1792=0.071

Hence, the margin of error is 0.071.

04

Construct the confidence interval in the form of p^ ± E

The confidence interval in the form of p^卤Eis given as:

p^-E<p<p^+E0.25-0.071<p<0.25+0.0710.179<p<0.321

Therefore, the confidence interval in the format p^卤Eis 0.25卤0.071.

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Most popular questions from this chapter

Constructing and Interpreting Confidence Intervals. In Exercises 13鈥�16, use the given sample data and confidence level. In each case, (a) find the best point estimate of the population proportion p; (b) identify the value of the margin of error E; (c) construct the confidence interval; (d) write a statement that correctly interprets the confidence interval.

In a study of the accuracy of fast food drive-through orders, McDonald鈥檚 had 33 orders that were not accurate among 362 orders observed (based on data from QSR magazine).

Construct a 95% confidence interval for the proportion of orders that are not accurate.

Determining Sample Size. In Exercises 31鈥�38, use the given data to find the minimum sample size required to estimate a population proportion or percentage.

Bachelor鈥檚 Degree in Four Years

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor鈥檚 degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.05 margin of error, and use a confidence level of 95%.

a. Assume that nothing is known about the percentage to be estimated.

b. Assume that prior studies have shown that about 40% of full-time students earn bachelor鈥檚 degrees in four years or less.

c. Does the added knowledge in part (b) have much of an effect on the sample size?

Confidence Intervals. In Exercises 9鈥�24, construct the confidence interval estimate of the mean. In Exercises 2-19,Mercury in SushiAn FDA guideline is that themercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D鈥橝gostino, Eli鈥檚 Manhattan, Fairway, Food Emporium, Gourmet Garage, Grace鈥檚 Marketplace, and Whole Foods. Construct a 98% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?

0.56 0.75 0.10 0.95 1.25 0.54 0.88

Mean Body Temperature Data Set 3 鈥淏ody Temperatures鈥� in Appendix B includes a sample of 106 body temperatures having a mean of 98.20掳F and a standard deviation of 0.62掳F. Construct a 95% confidence interval estimate of the mean body temperature for the entire population. What does the result suggest about the common belief that 98.6掳F is the mean body temperature?

In Exercises 5鈥�8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2R, and the confidence interval estimate of 蟽. The samples are from Appendix B and it is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Platelet Counts of Women 99% confidence;n= 147,s= 65.4.
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