Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 14.3, Problem 7E
To determine
State whether it can be concluded that a greater proportion drive in the slow lane than in the fast lane.
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2) A researcher is deciding between a sample size of n=250 and a sample of size n=500. Compared to using a sample size of n=500, a 95% confidence interval based on a sample size of n=250 will be *
A) narrower and would involve a larger risk of being incorrect.
B) wider and would involve a smaller risk of being incorrect.
C) wider and would involve a larger risk of being incorrect.
D) wider and would involve the same risk of being incorrect.
E) narrower and would have the same risk of being incorrect.
1. A recent survey showed that from a sample of 500 packages delivered by a Postal Service, 480were delivered on time.
a) Construct a 95% confidence interval for the proportion of all packages that are deliveredon time by the Postal Service.
For each of the following questions, indicate whether it is best assessed by using a confidence interval or a hypothesis test or whether statistical inference is not relevant to answer it. (answer all please!!)
Do a majority of adults riding a bicycle wear a helmet?
On average, how many more minutes do ladies spend in the restroom than men?
Is the median Exam 1 score for STA 270 students in section 10 any different from that of STA 270 students in section 11?
What is the average daily calorie intake of 20-year-old males?
In 2010, what percent of the US Senate voted to confirm Elena Kagan as a member of the Supreme Court?
Chapter 14 Solutions
Mathematical Statistics with Applications
Ch. 14.3 - Historically, the proportions of all Caucasians in...Ch. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10E
Ch. 14.3 - The data in the following table are the frequency...Ch. 14.4 - On the 40th anniversary of President John F....Ch. 14.4 - A study was conducted by Joseph Jacobson and Diane...Ch. 14.4 - Suppose that the entries in a contingency table...Ch. 14.4 - A survey to explore the relationship between...Ch. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - The results of a study suggest that the initial...Ch. 14.4 - Refer to Exercise 14.10. Test the hypothesis, at...Ch. 14.4 - An interesting and practical use of the 2 test...Ch. 14.5 - A study to determine the effectiveness of a drug...Ch. 14.5 - The 2 test used in Exercise 14.22 is equivalent to...Ch. 14.5 - How do Americans in the sandwich generation...Ch. 14.5 - Does education really make a difference in how...Ch. 14.5 - A manufacturer of buttons wished to determine...Ch. 14.5 - Traditionally, U.S. labor unions have been content...Ch. 14.5 - Prob. 29ECh. 14.5 - Refer to Exercise 14.29. Estimate the difference...Ch. 14.5 - A survey was conducted to investigate interest of...Ch. 14 - Prob. 32SECh. 14 - A survey was conducted to determine student,...Ch. 14 - How would you rate yourself as a driver? According...Ch. 14 - Prob. 35SECh. 14 - Knee injuries are a major problem for athletes in...Ch. 14 - It is often not clear whether all properties of a...Ch. 14 - Prob. 39SECh. 14 - Prob. 40SECh. 14 - Prob. 41SECh. 14 - Prob. 42SECh. 14 - Prob. 43SE
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- Consider the following two clinical trials concerning an investigational drug given for the treatment of cancer. #1: 100 people are administered the drug and 40 of the people respond. #2: 60 people are administered the drug and 24 of those people respond. Both trials have a 40% response rate. Construct a 95% confidence interval for the response rate for each trial. Which trial has a narrower confidence interval? a. Clinical trial #1 b. Clinical trial #2 c. The confidence intervals are the same width d. Unable to determine without additional informationarrow_forwardA U.S. Food Survey showed that Americans routinely eat beef in their diet. Suppose that in a study of 49 consumers in Illinois and 64 consumers in Texas the following results were obtained from two samples regarding average yearly beef consumption: Illinois Texas = 49 = 64 = 54.1lb = 60.4lb S1 = 7.0 S2 = 8.0 Develop a 95% confidence Interval Estimate for the difference between the two population means.arrow_forwarda researcher was interested in comparing the amount of time watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. the summary statistics are as follows. Women x1=12.7 hours s1=3.9 hours n1=14 hours Men x2=14.1 hours s2=5.2 hours n2=17 hours Construct a 99% confidence interval for u1-u2, the difference between the mean amount of time watching television for women and the mean amount of time spent watching television for menarrow_forward
- The drug Viagra became available in the U.S. in May 1988, in the wake of an advertising campaign that was unprecedented in scope and intensity. A Gallup poll found that by the end of the first week of May, 643 out of 1,005 adults were aware that Viagra was an impotency medication. a) Is the sample size large enough to compute a confidence interval for the proportion of adults who were aware that Viagra was an impotency medication after the first week of May? Yes, because more than 10 adults were not aware of Viagra Yes, because the sample size is greater than 30 Yes, because more than 10 adults were aware of Viagra Yes, because both np̂ and n(1-p̂) are greater than 10 b)Using the information from questions 1-3, suppose that p̂ is 0.40 and the standard error of p̂ is 0.10. Compute a 90% confidence interval for the proportion of adults that were aware of Viagra. (0.2355, 0.5645) (0.3, 0.5) (0.2355, 0.4) (0.3, 0.4)arrow_forwardA random sample of students at a college shows that 54 of 200 students had part-time jobs. Which of the follow-ing is the correct formula for a 90% confidence interval for the proportion of all students at this college withpart-time jobs?A) 0.27 { 1.28B10.27210.732200B) 0.27 { 1.28B10.5210.52200C) 0.27 { 1.645B10.27210.732200D) 0.27 { 1.645B10.5210.52200E) 0.27 { 1.96B10.27210.732200arrow_forwardquestion #2 2. A recent survey showed that from a sample of 500 packages delivered by a Postal Service,480 were delivered on time. a) Construct a 95% confidence interval for the proportion of all packages that are delivered on time by the Postal Service. b) The manager of the Postal Services claims that 98 percent of their mail are delivered on time. Test at the 1% significance level to determine whether the true proportion is less than 98 percent.arrow_forward
- In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and the United Kingdom. They found that a substantially greater percentage of U.K. ads use humor.a. Suppose that a random sample of 400 television ads in the United Kingdom reveals that 142 of these ads use humor. Find a point estimate of and a 95 percent confidence interval for the proportion of all U.K. television ads that use humor.b. Suppose a random sample of 500 television ads in the United States reveals that 122 of these ads use humor. Find a point estimate of and a 95 percent confidence interval for the proportion of all U.S. television ads that use humor.c. Do the confidence intervals you computed in parts a and b suggest that a greater percentage of U.K. ads use humor? Explain.arrow_forwardA 30 month study is conducted to determine the difference in rates of accidents per month between two departments in an assembly plant. If a sample of 12 from the first department averaged 12.3 accidents per month with a standard deviation of 3.5, and a sample of 9 from the second department averaged 7.6 accidents per month with standard deviation of 3.4, find: The t-value for a 95% confidence interval is: A. 2.09302 B. 1.724718 C. 2.08596 D. 1.729133 E. none of the precedingarrow_forwardA poll conducted in January 2020 surveyed likely democrat primary voters about who they would vote for in the primary election in 2020 and found the following results for the top 4 candidates: Joe Biden: 18% Bernie Sanders: 17% Elizabeth Warren: 16% Pete Buttigieg: 14% With a margin of error (AKA a 95% confidence interval) of ±4.1%. From a statistical standpoint, who would likely win the democrat primary if it was held on the day of the survey?arrow_forward
- In exploring possible sites for a convenience store in a large neighbourhood, the retail chain wants to know the proportion of ratepayers in favour of the proposal. If the estimate is required to be within 0.1 of the true proportion, would a random sample of size n = 100 from the council records be sufficient for a 95% confidence interval of this precision?arrow_forwardA statistics student wants to conduct a study to determine the proportion of workers in Cititon who commute to another town for work. If the student wants a 90% confidence interval with a margin of error of 2%, how many workers should be in her sample?arrow_forwardA research group studying cell phone habits asked the question “Do you ever use your cell phone to make a payment at a convenience store?” to people selected from two random samples of cell phone users. One sample consisted of older adults, ages 35 years and older, and the other sample consisted of younger adults, ages 18 years to 34 years. The proportion of people who answered yes in each sample was used to create a 95 percent confidence interval of (0.097,0.125)(0.097,0.125) to estimate the difference (younger minus older) between the population proportions of people who would answer yes to the question. Which of the following is the best description of what is meant by 95 percent confidence? In repeated random sampling with the same sample size, approximately 95% of the sample proportions from the younger group will be between 0.097 and 0.125 greater than the sample proportion from the older group. A In repeated random sampling with the same sample size,…arrow_forward
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