Section 7.1 Homework
The data given to the right includes data from 39 candies, and 9 of them are red. The company that makes the candy claims that 34% of its candies are red. Use the sample data to construct a 90% confidence interval estimate of the percentage of red candies. What do you conclude about the claim of 34%?
12.0% <p< 34.2% Yes, because the confidence interval includes 34%.
Which of the following is NOT needed to determine the minimum sample size required to estimate a population proportion?
Standard deviation
A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 11% chose chocolate pie, and the margin of error was given as ±55 percentage points. Describe what is meant by the statement that "the margin of error was given as ±55 percentage points."
The statement indicates that the interval 11% ±55% is likely to contain the true population percentage of people that prefer chocolate pie.
Express the confidence interval (0.083,0.145) in the form of p̂−E<p<p̂+E.
0.083 <p< 0.145
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 360 babies were born, and 324 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?
0.859 <p< 0.941 Yes, the proportion of girls is significantly different from 0.5.
A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 13% chose chocolate pie, and the margin of error was given as ±44 percentage points. Given specific sample data, which confidence interval is wider: the 99% confidence interval or the 80% confidence interval? Why is it wider?
A 99% confidence interval must be wider than an 80% confidence interval in order to be more confident that it captures the true value of the population proportion.
Which of the following is NOT an observation about critical values?
A critical value is the area in the right-tail region of the standard normal curve.
Which of the following groups has terms that can be used interchangeably with the others?
Percentage, Probability, and Proportion
A newspaper provided a "snapshot" illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company. The margin of error was given as 3±3 percentage points. What important feature of the poll was omitted?
The confidence level
When analyzing polls, which of the following is NOT a consideration?
The sample should be a voluntary response or convenience sample.
Which of the following is NOT a requirement for constructing a confidence interval for estimating the population proportion?
The trials are done without replacement.
Which concept below is NOT a main idea of estimating a population proportion?
Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.
A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4746 patients treated with the drug, 103 developed the adverse reaction of nausea. Construct a 95% confidence interval for the proportion of adverse reactions. 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. Choose the correct answer below.
a. 0.022 b. 0.004 c. 0.018 <p< 0.026 d. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
A study of 420,088 cell phone users found that 132 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0217% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell phones? Why or why not?
a. 0.026% <p < 0.037% b. Yes, because 0.0217% is not included in the confidence interval.
In a study of the accuracy of fast food drive-through orders, Restaurant A had 230 accurate orders and 63 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.198 <p< 0.279. What do you conclude?
a. 0.175 <p< 0.255 b. Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.
A genetic experiment with peas resulted in one sample of offspring that consisted of 444 green peas and 160 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?
a. 0.23 <p< 0.3 b. No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 345 trials, the touch therapists were correct 165 times. Complete parts (a) through (d). a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? b. Using Emily's sample results, what is the best point estimate of the therapists' success rate? c. Using Emily's sample results, construct a 95% confidence interval estimate of the proportion of correct responses made by touch therapists. d. What do the results suggest about the ability of touch therapists to select the correct hand by sensing energy fields?
a. 0.5 b. 0.478 c. 0.425 <p< 0.531 d. Since the confidence interval is not entirely above 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields.
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2369 subjects randomly selected from an online group involved with ears. 1199 surveys were returned. Construct a 95% confidence interval for the proportion of returned surveys. 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. Choose the correct answer below.
a. 0.506 b. 0.020 c. 0.486 <p< 0.526 d. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=937 and x=543 who said "yes." Use a 99% confidence level. 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. Choose the correct answer below.
a. 0.580 b. E= 0.042 c. 0.538 <p< 0.622 d. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than two percentage points? a) Assume that nothing is known about the percentage of computers with new operating systems. b) Assume that a recent survey suggests that about 86% of computers use a new operating system. c) Does the additional survey information from part (b) have much of an effect on the sample size that is required?
a. n= 1691 b. n= 815 c. Yes, using the additional survey information from part (b) dramatically reduces the sample size.
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's 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 prior studies have shown that about 45% of full-time students earn bachelor's degrees in four years or less. c. Does the added knowledge in part (b) have much of an effect on the sample size?
a. n= 384 b. n= 380 c. No, using the additional survey information from part (b) only slightly reduces the sample size.
You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 99% confident that the sample percentage is within 4.5 percentage points of the true population percentage. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. b. Assume that a prior survey suggests that about 33% of air passengers prefer an aisle seat. *replace .25 with .33(1-.33)
a. n= 822 b. n= 727
A _______ is a single value used to approximate a population parameter.
point estimate
Express the confidence interval 0.222<p<0.666 in the form p̂±E.
p̂±E= 0.444 ± 0.222
Find the critical value zα/2 that corresponds to the confidence level 81%.
zα/2equals= 1.31
Find the critical value zα/2 that corresponds to the given confidence level. 84%
zα/2equals= 1.41
Find the critical value zα/2 that corresponds to the given confidence level. 88%
zα/2equals= 1.55
