Stats Chapter 8
A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000. Provide a 97% confidence interval estimate for the average daily sale.
$193,490 to $206,510
A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000. Provide a 95% confidence interval estimate for the average daily sale.
$194,120 to $205,880
A random sample of 26 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $45. The balances of all checking accounts at the bank are normally distributed. Develop a 95% confidence interval estimate for the mean of the population.
$281.82 to $318.18
The monthly incomes from a random sample of faculty at a university are shown below. Monthly Income ($1000s) 3.0 4.0 6.0 3.0 5.0 5.0 6.0 8.0 Compute a 90% confidence interval for the mean of the population. The population of all faculty incomes is known to be normally distributed. Give your answer in dollars.
$3,867.52 to $6,132.48
The monthly incomes from a random sample of faculty at a university are shown below. Monthly Income ($1000s) 3.0 4.0 6.0 3.0 5.0 5.0 6.0 8.0 Compute a 90% confidence interval for the mean of the population. The population of all faculty incomes is known to be normally distributed. Give your answer in dollars.
$3,867.52 to $6,132.48
In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the population proportion. Interpret your results.
.199 to .261 With a 90% level of confidence we can state that the proportion of all college students who read or watch the news every day is between .199 and .261.
In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined. If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean?
1951 to 2049
A sample of 100 cans of coffee showed an average weight of 13 ounces. The population standard deviation is 0.8 ounce. Discuss why the answers in parts (a) and (b) are different.
As the level of confidence increases, the confidence interval becomes wider.
A random sample of 25 observations was selected from a normally distributed population. The average in the sample was 84.6 with a variance of 400. Discuss why the 90% and 99% confidence intervals are different.
As the level of confidence increases, the confidence interval gets wider.
The mean of the t distribution is _____. a. 0 b. .5 c. 1 d. dependent upon the sample size
a. 0
A sample of 100 cans of coffee showed an average weight of 13 ounces. The population standard deviation is 0.8 ounce. a. Construct a 95% confidence interval for the mean of the population. b. Construct a 95.44% confidence interval for the mean of the population. c. Discuss why the answers in parts (a) and (b) are different.
a. 12.8432 to 13.1568 b. 12.84 to 13.16 c. As the level of confidence increases, the confidence interval becomes wider.
It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is a. 25 b. 74 c. 189 d. 75
d. 75
In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the population proportion. Interpret your results.
.199 to .261
A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 32 current students and discovers that 12 will return for summer school. Construct a 90% confidence interval estimate for the proportion of current spring students who will return for summer school.
.234 to .516
In a random sample of 400 registered voters, 120 indicated they plan to vote for Candidate A. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Candidate A.
.255 to .345
In a random sample of 200 registered voters, 120 indicated they are Democrats. Develop a 95% confidence interval for the proportion of registered voters in the population who are Democrats.
.5321 to .6679
The manager of University Credit Union (UCU) is concerned about checking account transaction discrepancies. Customers are bringing transaction errors to the attention of the bank's staff several months after they occur. The manager would like to know what proportion of his customers balance their checking accounts within 30 days of receiving a transaction statement from the bank. Using random sampling, 400 checking account customers are contacted by telephone and asked if they routinely balance their accounts within 30 days of receiving a statement. 271 of the 400 customers respond Yes. Develop a 95% confidence interval estimate for the proportion of the population of checking account customers at UCU who routinely balance their accounts in a timely manner.
.6775 ± .0458 or .6317 to .7233
A statistician selected a sample of 16 accounts receivable and determined the mean of the sample to be $5,000 with a standard deviation of $400. She reported that the sample information indicated the mean of the population ranges from $4,739.80 to $5,260.20. She did not report what confidence coefficient she had used. Based on the above information, determine the confidence coefficient that was used.
.98
A random sample of 49 lunch customers was selected at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes. Compute the standard error of the mean.
1.4286
A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that it mines. Assuming the company reports that the standard deviation of daily output is 200 tons, how many days should it sample so that the margin of error will be 39.2 tons or less?
100
A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 32 current students and discovers that 12 will return for summer school. With a .95 probability, what sample size would have to be selected to provide a margin of error of 3% or less?
1001
A simple random sample of 144 items resulted in a sample mean of 1080. The population standard deviation is known to be 240. Develop a 95% confidence interval for the population mean.
1040.8 to 1119.2
A simple random sample of 144 items resulted in a sample mean of 1080. The population standard deviation is known to be 240. Develop a 95% confidence interval for the population mean.
1040.8 to 1119.2
A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00. What is the 95% confidence interval of the population mean?
112.16 to 127.84
The monthly starting salaries of students who receive an MBA degree have a standard deviation of $110. What size sample should be selected to obtain a .95 probability of estimating the mean monthly income within $20 or less?
117
In order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours per week watching television. The standard deviation is 3.2 hours per week for all freshmen college students. Suppose the sample mean came from a sample of 25 students. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. Assume that the hours are normally distributed.
12.679 to 15.321
A sample of 100 cans of coffee showed an average weight of 13 ounces. The population standard deviation is 0.8 ounce. Construct a 95.44% confidence interval for the mean of the population.
12.84 to 13.16
A sample of 100 cans of coffee showed an average weight of 13 ounces. The population standard deviation is 0.8 ounce. Construct a 95% confidence interval for the mean of the population.
12.8432 to 13.1568
The standard deviation for the lifetimes of washing machines is estimated to be 800 hours. What sample size must be selected in order to be 97% confident that the margin of error will not exceed 50 hours?
1206
In order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours per week watching television. The standard deviation is 3.2 hours per week for all freshmen college students. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week.
13.608 to 14.392
The manager of University Credit Union (UCU) is concerned about checking account transaction discrepancies. Customers are bringing transaction errors to the attention of the bank's staff several months after they occur. The manager would like to know what proportion of his customers balance their checking accounts within 30 days of receiving a transaction statement from the bank. Using random sampling, 400 checking account customers are contacted by telephone and asked if they routinely balance their accounts within 30 days of receiving a statement. 271 of the 400 customers respond Yes. Suppose UCU wants a 95% confidence interval estimate of the population proportion with a margin of error of E = .025. What sample size is needed?
1343
A real estate agent wants to estimate the mean selling price of two-bedroom homes in a particular area. She wants to estimate the mean selling price to within $10,000 with an 89.9% level of confidence. The standard deviation of selling prices is unknown but the agent estimates that the highest selling price is $1,000,000 and the lowest is $50,000. How many homes should be sampled?
1518
In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 pounds. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
17.11 to 22.89
In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 pounds. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.
17.39 to 22.61
You are given the following information obtained from a random sample of four observations selected from a large, normally distributed population. 25 47 32 56 Construct a 95% confidence interval for μ.
17.613 to 62.387
You are given the following information obtained from a random sample of four observations selected from a large, normally distributed population. 25 47 32 56 Construct a 95% confidence interval for the mean of the population.
17.613 ≤ μ ≤ 62.387
A sample of 16 students from a large university is selected. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population. Assume the population of student ages is normally distributed.
18.8035 to 25.1965
The makers of a soft drink want to identify the average age of its consumers. A sample of 16 consumers is selected. The average age in the sample was 22.5 years with a standard deviation of 5 years. Assume the population of consumer ages is normally distributed. Construct a 95% confidence interval for the average age of all the consumers.
19.836 to 25.164
In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined. If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean.
1951 to 2049
The makers of a soft drink want to identify the average age of its consumers. A sample of 16 consumers is selected. The average age in the sample was 22.5 years with a standard deviation of 5 years. Assume the population of consumer ages is normally distributed. Construct an 80% confidence interval for the average age of all the consumers.
20.824 to 24.176
You are given the following information obtained from a random sample of four observations selected from a large, normally distributed population. 25 47 32 56 Construct a 90% confidence interval for μ.
23.445 to 56.555
The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers revealed an average age of 28 years with a standard deviation of 10 years. Determine a 95% confidence interval estimate for the average age of all his customers. Assume the population of customer ages is normally distributed.
23.872 to 32.128
A simple random sample of 25 items from a normally distributed population resulted in a sample mean of 28 and a standard deviation of 7.5. Construct a 95% confidence interval for the population mean.
24.904 to 31.096
In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined. Assume a population standard deviation of 350 kilowatt-hours. Determine the standard error of the mean.
25
In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined. Assume a population standard deviation of 350 kilowatt-hours. Determine the standard error of the mean.
25
The manager of a department store wants to determine what proportion of people who enter the store use the store's credit card for their purchases. What size sample should he take so that at 99% confidence the error will not be more than 8%?
260
If the standard deviation of the lifetimes of vacuum cleaners is estimated to be 300 hours, what sample size must be selected in order to be 97% confident that the margin of error will not exceed 40 hours?
265
A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The population standard deviation is known to be $60. Construct a 95% confidence interval estimate for the population mean.
269.31 to 290.69
A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The population standard deviation is known to be $60. Give a point estimate of the population mean.
280
For inventory purposes, a grocery store manager wants to estimate the mean number of pounds of cat food sold per month. The estimate is desired to be within 10 pounds with a 95% level of confidence. A pilot study provided a standard deviation of 27.6 pounds. How many months should be sampled?
30
A sample of 25 patients in a doctor's office showed that they had to wait an average of 35 minutes with a standard deviation of 10 minutes before they could see the doctor. Provide a 98% confidence interval estimate for the average waiting time of all the patients who visit this doctor. Assume the population of waiting times is normally distributed.
30.016 to 39.984
A random sample of 49 lunch customers was selected at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes. Construct a 95% confidence interval for the true average amount of time customers spent in the restaurant.
30.20 to 35.80
A health club annually surveys its members. Last year, 33% of the members said they use the treadmill at least four times a week. How large a sample should be selected this year to estimate the percentage of members who use the treadmill at least four times a week? The estimate is desired to have a margin of error of 5% with a 95% level of confidence.
340
A local hotel wants to estimate the proportion of its guests that are from out of state. Preliminary estimates are that 45% of the hotel guests are from out-of-state.What sample size should be selected to estimate the proportion of out of state guests with a margin of error no larger than 5% and with a 95% level of confidence?
381
A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00. Determine the standard error of the mean.
4.00
Computer Services, Inc. wants to determine a confidence interval for the average CPU time of their teleprocessing transactions. A sample of 196 transactions yielded a mean of 5 seconds. The population standard deviation is 1.4 seconds. Determine a 97% confidence interval for the average CPU time.
4.783 to 5.217
Fifty students are enrolled in an Economics class. After the first examination, a random sample of five papers was selected. The grades were 60, 75, 80, 70, and 90. Calculate the estimate of the standard error of the mean.
4.79
You are given the following information obtained from a random sample of four observations selected from a large, normally distributed population. 25 47 32 56 What is the point estimate of μ?
40
A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be selected so that at 95% confidence the margin of error will be 2 months or less?
48
In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined. With a .95 probability, determine the margin of error.
49
In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined. With a .95 probability, determine the margin of error.
49
A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The population standard deviation is known to be $60. Find the standard error of the mean.
5.4545
A random sample of 81 children with working mothers showed that they were absent from school an average of 6 days per term. The population standard deviation is known to be 1.8 days. Provide a 90% confidence interval for the average number of days absent per term for all children with working mothers.
5.671 to 6.329
The Highway Safety Department wants to study the driving habits of individuals. A sample of 41 cars traveling on the highway revealed an average speed of 60 miles per hour and a standard deviation of 7 miles per hour. The population of car speeds is approximately normally distributed. Determine a 90% confidence interval estimate for the speed of all cars.
58.16 to 61.84
A random sample of 49 lunch customers was selected at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes. With a .95 probability, what sample size would have to be selected to provide a margin of error of 2.5 minutes or less?
62
Fifty students are enrolled in an Economics class. After the first examination, a random sample of five papers was selected. The grades were 60, 75, 80, 70, and 90. If there were 200 students in the class, what would be the 90% confidence interval for the mean grade of all the students in the class?
64.34 to 85.66
Fifty students are enrolled in an Economics class. After the first examination, a random sample of five papers was selected. The grades were 60, 75, 80, 70, and 90. Assume the assumption of part (b) is met. Provide a 90% confidence interval for the mean grade of all the students in the class.
64.783 to 85.217
A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00. With a .95 probability, determine the margin of error.
7.84
A random sample of 25 observations was selected from a normally distributed population. The average in the sample was 84.6 with a variance of 400. Construct a 99% confidence interval for μ.
73.412 to 95.788
A random sample of 25 observations was selected from a normally distributed population. The average in the sample was 84.6 with a variance of 400. Construct a 90% confidence interval for μ.
77.756 to 91.444
The manager of Hudson Auto Repair wants to advertise one price for an engine tune-up, with parts included. Before he decides the price to advertise, he needs a good estimate of the average cost of tune-up parts. A sample of 20 customer invoices for tune-ups has been selected and the costs of parts, rounded to the nearest dollar, are listed below. 91 78 93 57 75 52 99 80 105 62 104 74 62 68 97 73 77 65 80 109 Provide a 90% confidence interval estimate of the mean cost of parts per tune-up for all of the tune-ups performed at Hudson Auto Repair.
80.05 ± 6.54 or 73.51 to 86.59
The average monthly electric bill of a random sample of 256 residents of a city is $90. The population standard deviation is assumed to be $24. Construct a 95% confidence interval for the mean monthly electric bills of all residents.
87.06 to 92.94
The average monthly electric bill of a random sample of 256 residents of a city is $90. The population standard deviation is assumed to be $24. Construct a 90% confidence interval for the mean monthly electric bills of all residents.
87.5325 to 92.4675
It is known that the variance of a population equals 484. A random sample of 81 observations is going to be selected from the population. With an .80 probability, what sample size would have to be selected to provide a margin of error of 3 or less?
89
A random sample of 81 students at a local university showed that they work an average of 100 hours per month. The population standard deviation is known to be 27 hours. Compute a 95% confidence interval for the mean hours per month all students at the university work.
94.12 to 105.88
The makers of a soft drink want to identify the average age of its consumers. A sample of 16 consumers is selected. The average age in the sample was 22.5 years with a standard deviation of 5 years. Assume the population of consumer ages is normally distributed. Discuss why the 95% and 80% confidence intervals are different.
As the level of confidence increases, the confidence interval gets wider.
You are given the following information obtained from a random sample of four observations selected from a large, normally distributed population. 25 47 32 56 Discuss why the 90% and 95% confidence intervals are different.
As the level of confidence increases, the confidence interval gets wider.
A random sample of 25 observations was selected from a normally distributed population. The average in the sample was 84.6 with a variance of 400. What would you expect to happen to the confidence interval in part (a) if the sample size was increased? Be sure to explain your answer.
Decrease in width since the margin of error decreased.
A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The population standard deviation is known to be $60. Is it necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances? Explain.
No, since the sample means will be normally distributed by the central limit theorem.
A random sample of 49 lunch customers was selected at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes. What can be said about the sampling distribution for the average amount of time customers spent in the restaurant? Be sure to explain your answer.
Normal by the central limit theorem
Fifty students are enrolled in an Economics class. After the first examination, a random sample of five papers was selected. The grades were 60, 75, 80, 70, and 90. What assumption must be made before we can determine an interval for the mean grade of all the students in the class? Explain why.
Since the sample is small (n < 30) and σ is estimated from s, we must assume the distribution of all the grades is normal.
Political Science, Inc. (PSI) specializes in voter polls and surveys designed to keep political office seekers informed of their position in a race. Using telephone surveys, interviewers ask registered voters who they would vote for if the election were held that day. In a recent election campaign, PSI found that 220 registered voters, out of 500 contacted, favored a particular candidate. Suppose that PSI would like 99% confidence that the sample proportion is within ± .03 of the population proportion. What sample size is needed to provide the desired margin of error?
The required sample size is 1816.
It is known that the variance of a population equals 484. A random sample of 81 observations is going to be selected from the population. With an .80 probability, what statement can be made about the size of the margin of error?
There is a .80 probability that the sample mean will provide a margin of error of 3.129 or less.
A random sample of 49 lunch customers was selected at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes. With a .95 probability, what statement can be made about the size of the margin of error?
There is a .95 probability that the sample mean will provide a margin of error of 2.80 or less.
A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was selected of 10 one-bedroom units within a half-mile of campus and the rents paid. The sample mean is $550 and the sample standard deviation is $60.05. Provide a 95% confidence interval estimate of the mean rent per month for the population of one- bedroom units within a half-mile of campus. Assume this population is normally distributed.
We are 95% confident that the mean rent per month for the population of one-bedroom units within a half-mile of campus is between $507.05 and $592.95.
Political Science, Inc. (PSI) specializes in voter polls and surveys designed to keep political office seekers informed of their position in a race. Using telephone surveys, interviewers ask registered voters who they would vote for if the election were held that day. In a recent election campaign, PSI found that 220 registered voters, out of 500 contacted, favored a particular candidate. Develop a 95% confidence interval estimate for the proportion of the population of registered voters that favors the candidate.
We are 95% confident that the proportion of the population of registered voters that favors the candidate is between .3965 and .4835.
A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The population standard deviation is known to be $60. Interpret the confidence interval estimate that you constructed in part (d).
With a 95% level of confidence, we can state that the average daily balance of all checking accounts at this bank is between $269.31 and $290.69.
A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000. a. Provide a 95% confidence interval estimate for the average daily sale. b. Provide a 97% confidence interval estimate for the average daily sale.
a. $194,120 to $205,880 b. $193,490 to $206,510
In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. With a .95 probability, the margin of error is approximately_____. a. .26 b. 1.96 c. .21 d. 1.64
a. .26
A random sample of 49 lunch customers was selected at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes. a. Compute the standard error of the mean. b. What can be said about the sampling distribution for the average amount of time customers spent in the restaurant? Be sure to explain your answer. c. With a .95 probability, what statement can be made about the size of the margin of error? d. Construct a 95% confidence interval for the true average amount of time customers spent in the restaurant. e. With a .95 probability, what sample size would have to be selected to provide a margin of error of 2.5 minutes or less?
a. 1.4286 b. Normal by the central limit theorem c. There is a .95 probability that the sample mean will provide a margin of error of 2.80 or less. d. 30.20 to 35.80 e. 62
In order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours per week watching television. The standard deviation is 3.2 hours per week for all freshmen college students. a. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. b. Suppose the sample mean came from a sample of 25 students. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. Assume that the hours are normally distributed.
a. 13.608 to 14.392 b. 12.679 to 15.321
In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 pounds. a. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage. b. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.
a. 17.11 to 22.89 b. 17.39 to 22.61
The makers of a soft drink want to identify the average age of its consumers. A sample of 16 consumers is selected. The average age in the sample was 22.5 years with a standard deviation of 5 years. Assume the population of consumer ages is normally distributed. a. Construct a 95% confidence interval for the average age of all the consumers. b. Construct an 80% confidence interval for the average age of all the consumers. c. Discuss why the 95% and 80% confidence intervals are different.
a. 19.836 to 25.164 b. 20.824 to 24.176 c. As the level of confidence increases, the confidence interval gets wider.
A random sample of 36 students at a community college showed an average age of 25 years. Assume the ages of all students at the college are normally distributed with a standard deviation of 1.8 years. The 98% confidence interval for the average age of all students at this college is _____. a. 24.301 to 25.699 b. 24.385 to 25.615 c. 23.200 to 26.800 d. 23.236 to 26.764
a. 24.301 to 25.699
A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00. a. Determine the standard error of the mean. b. With a .95 probability, determine the margin of error. c. What is the 95% confidence interval of the population mean?
a. 25 b. 49 c. 1951 to 2049
A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00. a. Determine the standard error of the mean. b. With a .95 probability, determine the margin of error. c. What is the 95% confidence interval of the population mean?
a. 4.00 b. 7.84 c. 112.16 to 127.84
You are given the following information obtained from a random sample of four observations selected from a large, normally distributed population. 25 47 32 56 a. What is the point estimate of μ? b. Construct a 95% confidence interval for μ. c. Construct a 90% confidence interval for μ. d. Discuss why the 90% and 95% confidence intervals are different.
a. 40 b. 17.613 to 62.387 c. 23.445 to 56.555 d. As the level of confidence increases, the confidence interval gets wider.
It is known that the variance of a population equals 1,936. A random sample of 121 has been selected from the population. There is a .95 probability that the sample mean will provide a margin of error of _____. a. 7.84 or less b. 31.36 or less c. 344.96 or less d. 1,936 or less
a. 7.84 or less
A random sample of 25 observations was selected from a normally distributed population. The average in the sample was 84.6 with a variance of 400. a. Construct a 90% confidence interval for μ. b. Construct a 99% confidence interval for μ. c. Discuss why the 90% and 99% confidence intervals are different. d. What would you expect to happen to the confidence interval in part (a) if the sample size was increased? Be sure to explain your answer.
a. 77.756 to 91.444 b. 73.412 to 95.788 c. As the level of confidence increases, the confidence interval gets wider. d. Decrease in width since the margin of error decreased.
The average monthly electric bill of a random sample of 256 residents of a city is $90. The population standard deviation is assumed to be $24. a. Construct a 90% confidence interval for the mean monthly electric bills of all residents. b. Construct a 95% confidence interval for the mean monthly electric bills of all residents.
a. 87.5325 to 92.4675 b. 87.06 to 92.94
A bank manager wishes to estimate the average waiting time for customers in line for tellers. A random sample of 50 times is measured and the average waiting time is 5.7 minutes. The population standard deviation of waiting time is 2 minutes. Which Excel function would be used to construct a confidence interval estimate? a. CONFIDENCE.NORM b. NORM.INV c. T.INV d. INT
a. CONFIDENCE.NORM
A newspaper wants to estimate the proportion of Americans who will vote for Candidate A. A random sample of 1000 voters is selected. Of the 1000 respondents, 526 say that they will vote for Candidate A. Which Excel function would be used to construct a confidence interval estimate? a. NORM.S.INV b. NORM.INV c. T.INV d. INT
a. NORM.S.INV
A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The population standard deviation is known to be $60. a. Is it necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances? Explain. b. Find the standard error of the mean. c. Give a point estimate of the population mean. d. Construct a 95% confidence interval estimate for the population mean. e. Interpret the confidence interval estimate that you constructed in part (d).
a. No, since the sample means will be normally distributed by the central limit theorem. b. 5.4545 c. 280 d. 269.31 to 290.69 e. With a 95% level of confidence, we can state that the average daily balance of all checking accounts at this bank is between $269.31 and $290.69.
It is known that the variance of a population equals 484. A random sample of 81 observations is going to be selected from the population. a. With an .80 probability, what statement can be made about the size of the margin of error? b. With an .80 probability, what sample size would have to be selected to provide a margin of error of 3 or less?
a. There is a .80 probability that the sample mean will provide a margin of error of 3.129 or less. b. 89
A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to .90, the interval for μ _____. a. becomes narrower b. becomes wider c. does not change d. becomes .1
a. becomes narrower
The ability of an interval estimate to contain the value of the population parameter is described by the _____. a. confidence level b. degrees of freedom c. precise value of the population mean μ d. None of the answers is correct.
a. confidence level
For the interval estimation of μ when σ is assumed known, the proper distribution to use is the_____. a. standard normal distribution b. t distribution with n degrees of freedom c. t distribution with n − 1 degrees of freedom d. t distribution with n − 2 degrees of freedom
a. standard normal distribution
In general, higher confidence levels provide _____. a. wider confidence intervals b. narrower confidence intervals c. a smaller standard error d. unbiased estimates
a. wider confidence intervals
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the _____. a. width of the confidence interval to increase b. width of the confidence interval to decrease c. width of the confidence interval to remain the same d. sample size to increase
a. width of the confidence interval to increase
Computing the necessary sample size for an interval estimate of a population proportion requires a planning value for p. In case of any uncertainty about an appropriate planning value, we know the value that will provide the largest sample size for a given level of confidence and a given margin of error is a. .10 b. .50 c. .90 d. 1
b. .50
The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to _____. a. .01 b. .50 c. .51 d. .99
b. .50
A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is _____. a. 15.2 to 24.8 b. 19.2 to 20.8 c. 19.216 to 20.784 d. 21.2 to 22.8
b. 19.2 to 20.8
The t value with a 95% confidence and 24 degrees of freedom is _____. a. 1.711 b. 2.064 c. 2.492 d. 2.069
b. 2.064
The t value with a 95% confidence and 24 degrees of freedom is _____. a. 1.711 b. 2.064 c. 2.492 d. 2.069
b. 2.064
The use of the normal probability distribution as an approximation of the sampling distribution of condition that both np and n(1 - p) equal or exceed _____. is based on the a. .05 b. 5 c. 15 d. 30
b. 5
The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed _____. a. .05 b. 5 c. 15 d. 30
b. 5
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. The 86.9% confidence interval for μ is _____. a. 46.500 to 73.500 b. 57.735 to 62.265 c. 59.131 to 60.869 d. 50 to 70
b. 57.735 to 62.265
An auto manufacturer wants to estimate the annual income of owners of a particular model of automobile. A random sample of 200 current owners is selected. The population standard deviation is known. Which Excel function would NOT be appropriate to use to construct a confidence interval estimate? a. NORM.S.INV b. COUNTIF c. AVERAGE d. STDEV
b. COUNTIF
A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid? a. 95% of the sample of employees has a systolic blood pressure between 123 and 139. b. If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure. c. 95% of the population of employees has a systolic blood pressure between 123 and 139. d. If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.
b. If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
Whenever using the t distribution in interval estimation, we must assume that _____. a. the sample size is less than 30 b. a random sample was selected c. the population is approximately normal d. the finite population correction factor is necessary
b. a random sample was selected
Whenever using the t distribution in interval estimation, we must assume that _____. a. the sample size is less than 30 b. a random sample was selected c. the population is approximately normal d. the finite population correction factor is necessary
b. a random sample was selected
Fifty students are enrolled in an Economics class. After the first examination, a random sample of five papers was selected. The grades were 60, 75, 80, 70, and 90. a. Calculate the estimate of the standard error of the mean. b. What assumption must be made before we can determine an interval for the mean grade of all the students in the class? Explain why. c. Assume the assumption of part (b) is met. Provide a 90% confidence interval for the mean grade of all the students in the class. d. If there were 200 students in the class, what would be the 90% confidence interval for the mean grade of all the students in the class?
b. a. 4.79 Since the sample is small (n < 30) and σ is estimated from s, we must assume the distribution of all the grades is normal. c. 64.783 to 85.217 d. 64.34 to 85.66
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____. a. becomes larger b. becomes smaller c. stays the same d. None of the answers is correct.
b. becomes smaller
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____. a. becomes larger b. becomes smaller c. stays the same d. None of the answers is correct.
b. becomes smaller
Using α = .04, a confidence interval for a population proportion is determined to be .65 to .75. If the level of significance is decreased, the interval for the population proportion _____. a. becomes narrower b. becomes wider c. does not change d. Not enough information is provided to answer this question.
b. becomes wider
When the level of confidence increases, the confidence interval _____. a. stays the same b. becomes wider c. becomes narrower d. cannot be determined from the information given
b. becomes wider
As the sample size increases, the margin of error _____. a. increases b. decreases c. stays the same d. None of the answers is correct.
b. decreases
An estimate of a population parameter that provides an interval believed to contain the value of the parameter is known as the _____. a. confidence level b. interval estimate c. parameter value d. population estimate
b. interval estimate
As the degrees of freedom increase, the t distribution approaches the _____ distribution. a. uniform b. normal c. exponential d. p
b. normal
The margin of error in an interval estimate of the population mean is a function of all of the following EXCEPT _____. a. level of significance b. sample mean c. sample size d. variability of the population
b. sample mean
The t distribution should be used whenever _____. a. the sample size is less than 30 b. the sample standard deviation is used to estimate the population standard deviation c. the population is not normally distributed d. None of the answers is correct.
b. the sample standard deviation is used to estimate the population standard deviation
We can reduce the margin of error in an interval estimate of p by doing any of the following EXCEPT _____. a. increasing the sample size b. using a planning value p* closer to .5 c. increasing the level of significance d. reducing the confidence coefficient
b. using a planning value p* closer to .5
We can reduce the margin of error in an interval estimate of p by doing any of the following EXCEPT _____. a. increasing the sample size b. using a planning value p* closer to .5 c. increasing the level of significance d. reducing the confidence coefficient
b. using a planning value p* closer to .5
The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. The standard error of the mean equals _____. a. .001 b. .01 c. .1 d. 1
c. .1
The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. With a .95 probability, the sample mean will provide a margin of error of _____. a. .95 b. .10 c. .196 d. 1.96
c. .196
If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____. a. .1 b. .95 c. .9 d. .05
c. .9
If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____. a. .1 b. .95 c. .9 d. .05
c. .9
If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is _____. a. .485 b. 1.96 c. .95 d. 1.645
c. .95
If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is _____. a. .485 b. 1.96 c. .95 d. 1.645
c. .95
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. If we are interested in determining an interval estimate for μ at 86.9% confidence, the z value to use is _____. a. 1.96 b. 1.31 c. 1.51 d. 2.00
c. 1.51
The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. The 95% confidence interval for the average checkout time for all customers is _____. a. 3 to 5 b. 1.36 to 4.64 c. 2.804 to 3.196 d. 1.04 to 4.96
c. 2.804 to 3.196
A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for μ is _____. a. 6.000 to 14.000 b. 9.846 to 10.154 c. 8.384 to 11.616 d. 8.462 to 11.538
c. 8.384 to 11.616
A manufacturer wants to estimate the proportion of defective items that are produced by a certain machine. A random sample of 50 items is selected. Which Excel function would NOT be appropriate to construct a confidence interval estimate? a. NORM.S.INV b. COUNTIF c. STDEV d. All of these answers are correct.
c. STDEV
From a population that is not normally distributed and whose standard deviation is not known, a sample of 50 items is selected to develop an interval estimate for μ. Which of the following statements is true? a. The standard normal distribution can be used. b. The t distribution with 50 degrees of freedom must be used. c. The t distribution with 49 degrees of freedom must be used. d. The sample size must be increased in order to develop an interval estimate.
c. The t distribution with 49 degrees of freedom must be used.
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. If the sample size was 25 (other factors remain unchanged), the interval for μ would _____. a. not change b. become narrower c. become wider d. become zero
c. become wider
The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the _____. a. level of significance b. confidence level c. confidence coefficient d. error factor
c. confidence coefficient
The confidence associated with an interval estimate is called the _____. a. level of significance b. degree of association c. confidence level d. precision
c. confidence level
The confidence associated with an interval estimate is called the _____. a. level of significance b. degree of association c. confidence level d. precision
c. confidence level
The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the _____. a. finite correction factor b. sample size c. degrees of freedom d. standard deviation
c. degrees of freedom
The general form of an interval estimate of a population mean or population proportion is the _____ plus or minus the _____. a. population mean, standard error b. level of significance, degrees of freedom c. point estimate, margin of error d. planning value, confidence coefficient
c. point estimate, margin of error
The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. If the confidence coefficient is reduced to .80, the standard error of the mean _____. a. will increase b. will decrease c. remains unchanged d. becomes negative
c. remains unchanged
In developing an interval estimate of the population mean, if the population standard deviation is unknown _____. a. it is impossible to develop an interval estimate b. a sample proportion can be used c. the sample standard deviation and t distribution can be used d. None of the answers is correct.
c. the sample standard deviation and t distribution can be used
In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. The standard error of the mean is _____. a. 7.5 b. .014 c. .160 d. .133
d. .133
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. The value to use for the standard error of the mean is _____. a. 13.5 b. 9 c. 2.26 d. 1.5
d. 1.5
To estimate a population mean, the sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is _____. a. 10 b. 11 c. 116 d. 117
d. 117
The z value for a 97.8% confidence interval estimation is _____. a. 2.02 b. 1.96 c. 2.00 d. 2.29
d. 2.29
A random sample of 144. Assuming the score is _____. of 25 statistics examinations was selected. The average score in the sample was 76 with a variance scores are normally distributed, the 99% confidence interval for the population average examination a. 70.02 to 81.98 b. 69.82 to 82.18 c. 70.06 to 81.94 d. 69.29 to 82.71
d. 69.29 to 82.71
A random sample of 25 statistics examinations was selected. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is _____. a. 70.02 to 81.98 b. 69.82 to 82.18 c. 70.06 to 81.94 d. 69.29 to 82.71
d. 69.29 to 82.71
In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. If the sample mean is 9 hours, then the 95% confidence interval is approximately _____. a. 7.04 to 110.96 hours b. 7.36 to 10.64 hours c. 7.80 to 10.20 hours d. 8.74 to 9.26 hours
d. 8.74 to 9.26 hours
An interval estimate is used to estimate _____. a. the shape of the population's distribution b. the sampling distribution c. a sample statistic d. a population parameter
d. a population parameter
To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT _____. a. desired margin of error b. confidence level c. population standard deviation d. degrees of freedom
d. degrees of freedom
To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT _____. a. desired margin of error b. confidence level c. population standard deviation d. degrees of freedom
d. degrees of freedom
We can use the normal distribution to make confidence interval estimates for the population proportion, p, when _____. a. np ≥ 5 b. n(1 − p) ≥ 5 c. p has a normal distribution d. np ≥ 5 and n(1 − p) ≥ 5
d. np ≥ 5 and n(1 − p) ≥ 5
For which of the following values of p is the value of P(1 − p) maximized? a. p = .99 b. p = .90 c. p = 1.0 d. p = .50
d. p = .50
The degrees of freedom associated with a t distribution are a function of the _____. a. area in the upper tail b. sample standard deviation c. confidence coefficient d. sample size
d. sample size
Whenever the population standard deviation is unknown, which distribution is used in developing an interval estimate for a population mean? a. standard distribution b. z distribution c. binomial distribution d. t distribution
d. t distribution
From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected. For the interval estimation of μ, the proper distribution to use is the _____. a. standard normal distribution b. z distribution c. t distribution with 26 degrees of freedom d. t distribution with 24 degrees of freedom
d. t distribution with 24 degrees of freedom
From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected. For the interval estimation of μ, the proper distribution to use is the _____. a. standard normal distribution b. z distribution c. t distribution with 26 degrees of freedom d. t distribution with 24 degrees of freedom
d. t distribution with 24 degrees of freedom
In determining the sample size necessary to estimate a population proportion, which of the following is NOT needed? a. the maximum margin of error that can be tolerated b. the confidence level required c. a preliminary estimate of the true population proportion p d. the mean of the population
d. the mean of the population
In determining the sample size necessary to estimate a population proportion, which of the following is NOT needed? a. the maximum margin of error that can be tolerated b. the confidence level required c. a preliminary estimate of the true population proportion p d. the mean of the population
d. the mean of the population
The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____. a. the sample size b. whether the population standard deviation is known c. whether the population has an approximately normal distribution d. whether there is sampling error
d. whether there is sampling error
The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____. a. the sample size b. whether the population standard deviation is known c. whether the population has an approximately normal distribution d. whether there is sampling error
d. whether there is sampling error
