busa3131 exam 3 hw
The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. Compute the 95% confidence interval for the population proportion.
0.35+-1.96*sqrt(0.35(1-0.35))/150
The proportion of dental procedures that are extractions is 0.16. Which of the following exemplifies a Type I error in this situation?
b. We reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually 0.16.
In interval estimation, as the sample size becomes larger, the interval estimate _____.
b. becomes narrower
The population parameter value and the point estimate differ because a sample is not a census of the entire population, but it is being used to develop the _____.
b. point estimate
The purpose of statistical inference is to make estimates or draw conclusions about a _____.
b. population based upon information obtained from the sample
The value of the _____ is used to estimate the value of the population parameter.
b. sample statistic
One reason a sample may fail to represent the population of interest is _____.
b. sampling error
The basis for using a normal probability distribution to approximate the sampling distribution of the sample means and population mean is _____.
b. the central limit theorem
When the expected value of the point estimator is equal to the population parameter it estimates, it is said to be _____.
b. unbiased
A pizza shop advertises that they deliver in 30 minutes or less or it is free. People who live in homes that are located on the opposite side of town believe it will take the pizza shop longer than 30 minutes to make and deliver the pizza. A random sample of 50 deliveries to homes across town was taken and the mean time was computed to be 32 minutes. What is the appropriate symbol to represent the value, 32?
b. x bar= 32
A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size _____.
d. n has the same probability of being selected
People end up tossing 12% of what they buy at the grocery store. Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. Calculate the sampling error of p , the proportion of groceries thrown out by your sample respondents. If required, round your answer to four decimal places.
0.014 exp: sqrt(0.12)(0.88)/540
The president of Doerman Distributors, Inc., believes that 30% of the firm's orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers. Assume that the president is correct and p = 0.30. What is the sampling error of p for this study? If required, round your answer to four decimal places.
0.0458 exp: sqrt (0.3*(1-0.3)/100)
A parameter is a numerical measure from a population, such as _____.
u
The random numbers generated using Excel's RAND function follows a _____ probability distribution between 0 and 1.
uniform
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. If we would like to capture the population mean with 95% confidence the margin of error would be _____.
2.262(9/sqrt10)
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. What is the standard error of the mean?
2.876
In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is _____.
23
The t value for a 99% confidence interval estimation based upon a sample of size 10 is _____.
3.249
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.
5.73-6.95
Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint.
60.54-81.46
For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent Mercer survey showed that 52% of U.S. employers were likely to require higher employee contributions for health care coverage. Suppose the survey was based on a sample of 400 companies. Compute the margin of error and a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage. If required, round your answer to four decimal places. Round intermediate calculations to four decimal places.
Margin of Error: 0.049 Confidence Interval: 0.4710 to 0.569
According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned. A Houston department store sampled 80 items sold in January and found that 9 of the items were returned. a) Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store. If required, round your answer to three decimal places. b) Construct a 95% confidence interval for the porportion of returns at the Houston store. If required, round your answer to three decimal places. c) Is the proportion of returns at the Houston store significantly different from the returns for the nation as a whole? Provide statistical support for your answer.
a) 0.113 b) 0.044 to 0.182 c) We reject the null hypothesis. We can conclude that the return rate for the Houston store is different than the U.S. national return rate.
The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011. Assume that the standard deviation for male graduates is $2.30, and for female graduates it is $2.05. a) What is the sampling error of x for a random sample of 50 male college graduates? If required, round your answer to four decimal places. b) What is the sampling error of x for a random sample of 50 female college graduates? If required, round your answer to four decimal places. c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller?
a) 0.3253 b) 0.2899 c) part b smaller for female... hourly wage is smaller for female exp: 2.30/sqrt 50, 2.05/sqrt 50
In a random sample of 400 registered voters, 120 indicated they plan to vote for Trump for President. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Trump.
b. (0.25, 0.34)
Larger values of α have the disadvantage of increasing the probability of making a _____.
b. Type I error
One of the questions in the Pew Internet & American Life Project asked adults if they used the Internet at least occasionally. The results showed that 454 out of 478 adults aged 18-29 answered Yes; 741 out of 833 adults aged 30-49 answered Yes; and 1,058 out of 1,644 adults aged 50 and over answered Yes. a) Develop a point estimate of the proportion of adults aged 18-29 who use the Internet. b) Develop a point estimate of the proportion of adults aged 30-49 who use the Internet. c) Develop a point estimate of the proportion of adults aged 50 and over who use the Internet. d) Comment on any apparent relationship between age and Internet use. e) Suppose your target population of interest is that of all adults (18 years of age and over). Develop an estimate of the proportion of that population who use the Internet.
a) 0.9498 b) 0.8896 c) 0.6436 d) younger e)0.7624 exp: a-c 454/478 e (454+741+1058)/(478+833+1644)
The College Board reported the following mean scores for the three parts of the SAT: Critical Reading 502 Mathematics 515 Writing 494 Assume that the population standard deviation on each part of the test is σ = 100. a) For a random sample of 30 test takers, what is the sampling error of x for scores on the Critical Reading part of the test? b) For a random sample of 60 test takers, what is the sampling error of x for scores on the Mathematics part of the test? c) For a random sample of 90 test takers, what is the sampling error of x for scores on the Writing part of the test?
a) 18.26 b) 12.91 c) 10.54 exp: 100/sqrt 30
Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 35% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. a) How many business owners in the survey plan to provide a holiday gift to their employees? b) Suppose the business owners in the sample do as they plan. Compute the p value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. If required, round your answer to four decimal places. If your answer is zero, enter "0". Do not round your intermediate calculations. c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts has decreased?
a) 21 b) 0.0437 c) We reject the null hypothesis. We can conclude that the proportion of business owners providing gifts has decreased., The smallest level of significance for which we could draw this conclusion is 0.01 because p-value is >= the corresponding α, we reject the null hypothesis.
A simple random sample of 5 months of sales data provided the following information: Month:1, 2, 3, 4, 5Units Sold: 94, 100, 85, 94, 92 a) Develop a point estimate of the population mean number of units sold per month. b) Develop a point estimate of the population standard deviation. If required, round your answer to two decimal places.
a) 93 b) 5.39 exp: [sq.rt (94-93)^2+...]/sq.rt 4
Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A research study will measure the cost of the new method over a sample production period. a) Develop the null and alternative hypotheses most appropriate for this study. b) Comment on the conclusion when H0 cannot be rejected. c) Comment on the conclusion when H0 can be rejected.
a) H0: >= 220 Ha: < 220 b) When H0 cannot be rejected, there is not enough evidence to conclude that the proposed manufacturing method reduces costs. c) When H0 can be rejected, there is enough evidence to conclude that the proposed manufacturing method reduce costs.
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. It is considering a promotion that involves mailing discount coupons to all its credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers. a) Choose the hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national. b) The file named Eagle contains the sample data. Develop a point estimate of the population proportion. If required, round your answer to two decimal places. c) Use α = 0.05 to conduct your hypothesis test. If required, round to two decimal places and -value to four decimal places.
a) Ho: <= 0.10 Ha: > 0.10 b) 0.13 c) z= 1.00, p= 0.1587 Because -value is > , we do not reject . We cannot conclude that more than 10% of Eagle Outfitters' credit card customers redeem their coupons. Based only on the obtained should not go national with the promotion.
Carpetland salespersons average $8,000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. a) Choose the appropriate null and alternative hypotheses. b) What is the Type I error in this situation? What are the consequences of making this error? c) What is the Type II error in this situation? What are the consequences of making this error?
a) Ho: <= 8000 Ha: > 8000 b) It would be concluding µ > 8,000 when the plan does not increase sales. This mistake could result in implementing the plan when it would not help. c) It would be concluding µ ≤ 8,000 when the plan does increase sales. This mistake could result in not implementing a plan that would increase sales.
What percentage of the population live in their state of birth? According to the U.S. Census Bureau's American Community Survey, the figure ranges from 25% in Nevada to 78.7% in Louisiana. The average percentage across all states and the District of Columbia is 57.7%. The data in the file Homestate are consistent with the findings in the American Community Survey. The data are for a random sample of 120 Arkansas residents and for a random sample of 180 Virginia residents. a) Choose the hypotheses that can be used to determine whether the percentage of stay-at-home residents in the two states differs from the overall average of 57.7%. b) Estimate the proportion of stay-at-home residents in Arkansas. If required, round your answer to four decimal places. c) Estimate the proportion of stay-at-home residents in Virginia. If required, round your answer to four decimal places. d) Would you expect the proportion of stay-at-home residents to be higher in Virginia than in Arkansas?
a) Ho: = 0.577 Ha: =/ 0.577 b) 0.6167, There is not sufficient evidence to conclude that the proportion of stay-at-home residents in Arkansas differs from the overall proportion of 0.577. c) 0.4944, There is sufficient evidence to conclude that the proportion of stay-at-home residents in Virginia differs from the overall proportion of 0.577. d) no, The sample results show that a higher percentage of current residents in Arkansas were born there then in Virginia.
The Port Authority sells a wide variety of cables and adapters for electronic equipment online. Last year the mean value of orders placed with the Port Authority was $47.28, and management wants to assess whether the mean value of orders placed to date this year is the same as last year. The values of a sample of 49,896 orders placed this year are collected and recorded in the file PortAuthority. a) Choose the hypotheses that can be used to test whether the mean value of orders placed this year differs from the mean value of orders placed last year. b) Use the data in the file PortAuthority to conduct your hypothesis test. What is the p value for your hypothesis test? If required, round your answer to four decimal places c) At α = 0.01, what is your conclusion?
a) Ho: =47.28 Ha: =/ 47.28 b) 0.0062 c) Reject H0. We can conclude that the population mean value of orders placed this year differs from the mean value of orders placed last year.
The national mean annual salary for a school administrator is $90,000 a year. A school official took a sample of 25 school administrators in the state of Ohio to learn about salaries in that state to see if they differed from the national average. a) Choose the hypotheses that can be used to determine whether the population mean annual administrator salary in Ohio differs from the national mean of $90,000. b) The sample data for 25 Ohio administrators is contained in the file named Administrator. What is the p value for your hypothesis test in part (a)? If required, round your answer to four decimal places. Do not round your intermediate calculations. c) At α = 0.05, can your null hypothesis be rejected?
a) Ho: =90000 Ha: =/ 90000 b) 0.0426 c) yes, There is sufficient evidence to conclude that the national mean annual salary for a school administrator in the state of Ohio differs from the national average.
Which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04. A sample of 100 neighborhood restaurants showed a mean price of $12.75 and a standard deviation of $2 for a comparable restaurant meal. a) Choose the appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than fixing a comparable meal at home. b) Using the sample from the 100 restaurants, what is the p value? If required, round your answer to four decimal places. c) At α = 0.05, what is your conclusion?
a) Ho: >- 13.04 Ha: <13.04 b) 0.0751 c) We fail to reject the null hypothesis. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.
Ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute indicate that the percentage is now 46%. a) Choose the appropriate hypotheses such that rejection of H0 will support the conclusion that a smaller proportion of American families own stocks or stock funds this year than 10 years ago. b) Assume the Investment Company Institute sampled 300 American families to estimate that the percent owning stocks or stock funds is 46% this year. What is the p value for your hypothesis test? If required, round your answer to four decimal places. Do not round your intermediate calculations. c) At α = 0.01, what is your conclusion?
a) Ho: >= 0.53 Ha: < 0.53 b) 0.0075 c) - Select your answer reject H0. We can conclude that a smaller proportion of American families own stocks or stock funds this year than they did 10 years ago.
Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour. a) Choose the appropriate null and alternative hypotheses if the mean cost for the current production method is $220 per hour. b) What is the Type I error in this situation? What are the consequences of making this error? c) What is the Type II error in this situation? What are the consequences of making this error?
a) Ho: >= 220 Ha: < 220 b) The Type I error is rejecting when it is true. This error occurs when it is concluded that the new production method reduces the mean operating cost per hour, when in fact it does not. This error could lead to implementing a production method that does not help to reduce operating costs. c) The Type II error is accepting H0 when it is false. This error occurs when it is concluded that the new production method does not reduce the mean operating cost per hour, when in fact it does. This error could lead to not implementing a production method that would have helped to reduce operating costs.
The Coca-Cola Company reported that the mean per capita annual sales of its beverages in the United States was 423 eight-ounce servings. Suppose you are curious whether the consumption of Coca-Cola beverages is higher in Atlanta, Georgia, the location of Coca-Cola's corporate headquarters. A sample of 36 individuals from the Atlanta area showed a sample mean annual consumption of 460.4 eight-ounce servings with a standard deviation of s = 101.9 ounces. a) Using α = 0.05, do the sample results support the conclusion that mean annual consumption of Coca-Cola beverage products is higher in Atlanta? b) What is your conclusion?
a) yes b) Reject the null hypothesis. We can conclude that Atlanta customers have a higher annual rate of consumption of Coca Cola beverages.
One of the questions on a survey of 1,000 adults asked if today's children will be better off than their parents. Representative data are shown in the file named ChildOutlook. A response of Yes indicates that the adult surveyed did think today's children will be better off than their parents. A response of No indicates that the adult surveyed did not think today's children will be better off than their parents. A response of Not Sure was given by 23% of the adults surveyed. a. What is the point estimate of the proportion of the population of adults who do think that today's children will be better off than their parents? If required, round your answer to two decimal places. b. At 95% confidence, what is the margin of error? If required, round your answer to four decimal places. c. What is the 95% confidence interval for the proportion of adults who do think that today's children will be better off than their parents? If required, round your answers to four decimal places. Do not round your intermediate calculations. d. What is the 95% confidence interval for the proportion of adults who do not think that today's children will be better off than their parents? If required, round your answers to four decimal places. Do not round your intermediate calculations. e. Which of the confidence intervals in parts (c) and (d) has the smaller margin of error? Why?
a. 0.24 b. 0.0265 c. 0.2135 to 0.2665 d. 0.4991 to 0.5609 e. part c, further from
According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 94 beat estimates, 29 matched estimates, and 39 fell short. a. What is the point estimate of the proportion that fell short of estimates? If required, round your answer to four decimal places. b. Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates. If required, round your answers to four decimal places. c. How large a sample is needed if the desired margin of error is 0.05? If required, round your answer to the next integer.
a. 0.2407 b. 0.0760, 0.5043 to 0.6562 c. 375
The Pew Research Center Internet Project conducted a survey of 857 Internet users. This survey provided a variety of statistics on them. a. The sample survey showed that 90% of respondents said the Internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. b. The sample survey showed that 67% of Internet users said the Internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends. c. Fifty-six percent of Internet users have seen an online group come together to help a person or community solve a problem, whereas only 25% have left an online group because of unpleasant interaction. Develop a 95% confidence interval for the proportion of Internet users who say online groups have helped solve a problem. d. Compare the margin of error for the interval estimates in parts (a), (b), and (c). How is the margin of error related to the sample proportion?
a. 0.8799 to 0.9201 b. 0.6385 to 0.7015 c. 0.5268 to 0.5932 d. increases
Which statement is NOT true?
a. Failing to reject the null hypothesis when it is false is a Type I error.
The owners of a fast food restaurant have automatic drink dispensers to help fill orders more quickly. When the 12 ounce button is pressed, they would like for exactly 12 ounces of beverage to be dispensed. There is, however, some variation in this amount. The company does not want the machine to systematically over fill or under fill the cups. Which of the following gives the correct set of hypotheses?
a. H0: u = 12, Ha: u ≠ 12
For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.
a. approximately normal for large sample sizes
Using an α = 0.04, a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion _____.
a. becomes wider
A one-tailed test is a hypothesis test in which the rejection region is _____.
a. in one tail of the sampling distribution
A null and alternative hypothesis for a one proportion z test are given as H0: p ≥ 0.8, Ha: p < 0.8. This hypothesis test is _____
a. lower-tailed
A simple random sample of 31 observations was taken from a large population. The sample mean equals 5. Five is a _____.
a. point estimate
The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion σp̄?
c. 0.039
The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the point estimate of the proportion of the population that logged onto Facebook that day?
c. 0.35
A large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time μ = 45 hours. The production manager has developed a new procedure for producing the part. He believes that the new procedure will decrease the population mean amount of time required to produce the part. After training a group of production line workers, a random sample of 25 parts will be selected and the average amount of time required to produce them will be determined. If the switch is made to the new procedure, the cost to implement the new procedure will be more than offset by the savings in manpower required to produce the parts. Use the hypotheses: H0: μ ≥ 45 hours and Ha: μ < 45 hours. If the sample mean amount of time is = 43.118 hours with the sample standard deviation s = 5.5 hours, give the appropriate conclusion, for α = 0.025.
c. Do not reject H0, do not switch to the new procedure.
A student wants to determine if pennies are really fair when flipped, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. If p denotes the true probability of a penny landing heads up when flipped, what are the appropriate null and alternative hypotheses?
c. H0: p = 0.5, Ha: p ≠ 0.5.
A pizza shop advertises that they deliver in 30 minutes or less or it is free. People who live in homes that are located on the opposite side of town believe it will take the pizza shop longer than 30 minutes to make and deliver the pizza. Write the null and alternative hypotheses that can be used to conduct a significance test.
c. H0: u ≤ 30, Ha: u > 30
The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are _____.
c. H0: u ≥ 50.1, Ha: u < 50.1
What are the two decisions that you can make from performing a hypothesis test?
c. Reject the null hypothesis; Fail to reject the null hypothesis
Determine whether the alternative hypothesis is left-tailed, right-tailed, or two-tailed: H0: μ = 11, Ha: μ > 11.
c. Right-tailed
A sample of 37 AA batteries had a mean lifetime of 584 hours. A 95% confidence interval for the population mean was 579.2 < μ < 588.8. Which statement is the correct interpretation of the results?
c. We are 95% confident that the mean lifetime of all the bulbs in the population is between 579.2 hours and 588.8 hours.
A Type I error is committed when _____.
c. a true null hypothesis is rejected
If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to _____.
c. be an unbiased estimator of the population parameter
An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the _____.
c. interval estimate
Two approaches to drawing a conclusion in a hypothesis test are _____.
c. p-value and critical value
A random sample selected from an infinite population is a sample selected such that each element selected comes from the same _____ and each element is selected _____.
c. population; independently
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. The 95% confidence interval for the true mean number of pushups that can be done is _____.
d. 8.56 to 21.40
As the number of degrees of freedom for a t distribution inceases, the difference between the t distribution and the standard normal distribution _____.
d. becomes smaller
You are _____ to commit a Type I error using the 0.05 level of significance than using the 0.01 level of significance.
d. more likely
The American League consists of 15 baseball teams. Suppose a sample of 5 teams is to be selected to conduct player interviews. The following table lists the 15 teams and the random numbers assigned by Excel's RAND function. Sort the table by random number from smallest to largest and select a sample of size 5.
new york, detroit, oakland, boston, kansas city
