Chapter 7.1 Homework

1.   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 percentage points. What important feature of the poll was​ omitted?

Choose the correct answer.

1. The confidence interval
2. the point estimate
3. The confidence level
4. The sample size

2.  A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 ​respondents, 13​% chose chocolate​ pie, and the margin of error was given as ±5 percentage points. Given specific sample​ data, which confidence interval is​ wider: the 99​% confidence interval or the 80​% confidence​ interval? Why is it​ wider?

Choose the correct answer below.

1. A 99​% confidence interval must be wider than an 80​% confidence interval because it contains 99​% of the true population​ parameters, while the 80​% confidence interval only contains 80​% of the true population parameters.
2. 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.
3. An 80​% confidence interval must be wider than a 99​% confidence interval because it contains​100%−80​%=20​% of the true population​ parameters, while the 99​% confidence interval only contains ​100%−99​%=1​% of the true population parameters.
4. An 80​% confidence interval must be wider than a 99​% confidence interval in order to be more confident that it captures the true value of the population proportion.

3.  Find the critical value 

that corresponds to the given confidence level.

99​%

4.  Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll,n=1088 and x=551 who said​ “yes.” Use a 95% confidence level.

​a) Find the best point estimate of the population proportion p.  _______  (Round to three decimal places as​ needed.)

​b) Identify the value of the margin of error E. _________ ​(Round to three decimal places as​ needed.)

​c) Construct the confidence interval . _____________< p < ___________

​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

1. One has 95​% confidence that the sample proportion is equal to the population proportion.
2. There is a 95​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
3. 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.
4. 95​% of sample proportions will fall between the lower bound and the upper bound.

5.  Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4147 patients treated with the​ drug, 192 developed the adverse reaction of nausea. Construct a 99​% confidence interval for the proportion of adverse reactions.

​a) Find the best point estimate of the population proportion p. _______ ​(Round to three decimal places as​ needed.)

​b) Identify the value of the margin of error E.  _______ ​(Round to three decimal places as​ needed.)

​c) Construct the confidence interval. ________ < p < ________   (Round to three decimal places as​ needed.)

​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

1. One has 99​% confidence that the sample proportion is equal to the population proportion.
2. There is a 99​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
3. 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.
4. 99​% of sample proportions will fall between the lower bound and the upper bound

6.  Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

In a study of cell phone use and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 2577 subjects randomly selected from an online group involved with ears. 1186 surveys were returned. Construct a 90​% confidence interval for the proportion of returned surveys.

​a) Find the best point estimate of the population proportion p.   _________ (Round to three decimal places as​ needed.)

​b) Identify the value of the margin of error E.  _________ ​(Round to three decimal places as​ needed.)

​c) Construct the confidence interval.  _______ <p< ____________ ​(Round to three decimal places as​ needed.)

​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

1. One has 90​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
2. There is a 90​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
3. One has 90​% confidence that the sample proportion is equal to the population proportion.
4. 90​% of sample proportions will fall between the lower bound and the upper bound.

7.   A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 584 babies were​ born, and 292 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?

_______________ <p< ____________   (Round to three decimal places as​ needed.)

Does the method appear to be​ effective?

1. Yes​, the proportion of girls is significantly different from 0.5.
2. No​, the proportion of girls is not significantly different from 0.5.

8.   A genetic experiment with peas resulted in one sample of offspring that consisted of 441 green peas and 153 yellow peas.

Construct a 95​% confidence interval to estimate of the percentage of yellow peas.

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?

Construct a 95​% confidence interval. Express the percentages in decimal form. _______ <p< ______  (Round to three decimal places as​ needed.)

Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

1. ​Yes, the confidence interval does not include​ 0.25, so the true percentage could not equal​ 25%
2. ​No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%

9.  In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 301 accurate orders and 62 that were not accurate.

Construct a 95​% confidence interval estimate of the percentage of orders that are not accurate.

Compare the results from part​ (a) to this 95​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.152<p<0.227. What do you​ conclude?

Construct a 95​% confidence interval. Express the percentages in decimal form. ______ <p< _______​(Round to three decimal places as​ needed.)

Choose the correct answer below.

1. No conclusion can be made because not enough information is given about the confidence interval for Restaurant B.
2. The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A.​ Therefore, Restaurant B has a significantly higher percentage of orders that are not accurate.
3. Since the upper confidence limit of the interval for Restaurant B is higher than both the lower and upper confidence limits of the interval for Restaurant​ A, this indicates that Restaurant B has a significantly higher percentage of orders that are not accurate.
4. Since the two confidence intervals​ overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.

10.  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 301 ​trials, the touch therapists were correct 142 times. Complete parts​ (a) through​ (d).

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? ______ ​(Type an integer or a decimal. Do not​ round.)

Using​ Emily’s sample​ results, what is the best point estimate of the​ therapists’ success​ rate? ______ ​(Round to three decimal places as​ needed.)

Using​ Emily’s sample​ results, construct a 90​% confidence interval estimate of the proportion of correct responses made by touch therapists. ______ <p<_____  ​(Round to three decimal places as​ needed.)

What do the results suggest about the ability of touch therapists to select the correct hand by sensing energy​ fields?

1. Since the confidence interval is not entirely below​ 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields.
2. Since the upper confidence limit is above​ 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields.
3. Since the lower confidence limit is below​ 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields.
4. 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

11.  In a survey of 3441 adults aged 57 through 85​ years, it was found that 86.4​% of them used at least one prescription medication. Complete parts​ (a) through​ (c) below.

How many of the 3441 subjects used at least one prescription​ medication? _______ ​(Round to the nearest integer as​ needed.)

Construct a​ 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication. _____ <p< ______ (Round to one decimal place as​ needed.)

What do the results tell us about the proportion of college students who use at least one prescription​ medication?

1. The results tell us​ that, with​ 90% confidence, the probability that a college student uses at least one prescription medication is in the interval found in part​ (b).
2. The results tell us that there is a​ 90% probability that the true proportion of college students who use at least one prescription medication is in the interval found in part​ (b).
3. The results tell us​ that, with​ 90% confidence, the true proportion of college students who use at least one prescription medication is in the interval found in part​ (b).
4. The results tell us nothing about the proportion of college students who use at least one prescription medication.

12.  A study of 420,016 cell phone users found that 137 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 0.0318​% for those not using cell phones. Complete parts​ (a) and​ (b).

Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. _______<p< _______ (Round to three decimal places as​ needed.)

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?

1. Yes​, because 0.0318​% is not included in the confidence interval.
2. Yes​, because 0.0318​% is included in the confidence interval.
3. No​, because 0.0318​% is not included in the confidence interval.
4. No​, because 0.0318​% is included in the confidence interval.

13 .  Refer to the data set of 20 randomly selected presidents given below. Treat the data as a sample and find the proportion of presidents who were taller than their opponents. Use that result to construct a​ 95% confidence interval estimate of the population percentage. Based on the​ result, does it appear that greater height is an advantage for presidential​ candidates? Why or why​ not?

Construct a​ 95% confidence interval estimate of the percentage of presidents who were taller than their opponents.  _______ <p< ____________  (Round to one decimal place as​ needed.)

If greater height was an​ advantage, then taller candidates should have won ______ ​50% of the elections. In this​ case, greater height _______ to be an advantage for presidential candidates because the confidence interval _____ include​ 50%.

14.  Fill in the blank. A critical​ value, 

   denotes the​ _______.

15.  Which of the following groups has terms that can be used interchangeably with the​ others?

Choose the correct answer below.

1. ​Percentage, Probability, and Proportion
2. Critical​ Value, Percentage, and Probability
3. Critical​ Value, Probability, and Proportion
4. Critical​ Value, Percentage, and Proportion

16.   Fill in the blank. A​ _______ is a single value used to approximate a population parameter.

17.  Which of the following is NOT a requirement for constructing a confidence interval for estimating the population​ proportion?

Choose the correct answer below.

1. There are at least 5 successes and 5 failures.  
2. The trials are done without replacement.
3. There are a fixed number of trials.
4. The sample is a simple random sample.