Stats test chapter 8

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 mean of the t distribution is _____. a. 0 b. .5 c. 1 d. dependent upon the sample size

0

Refer to Exhibit 8-2. The standard error of the mean equals _____. a. .001 b. .01 c. .1 d. 1

0.1

Refer to Exhibit 8-1. The standard error of the mean is _____. a. 7.5 b. .014 c. .160 d. .133

0.133

Refer to Exhibit 8-2. With a .95 probability, the sample mean will provide a margin of error of _____. a. .95 b. .10 c. .196 d. 1.96

0.196

Refer to Exhibit 8-1. With a .95 probability, the margin of error is approximately_____. a. .26 b. 1.96 c. .21 d. 1.64

0.26

Computing the necessary sample size for an interval estimate of a population proportion requires a planning value for . 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

0.50

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

0.50

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

0.9

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

0.95

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.

0.98

Refer to Exhibit 8-3. The value to use for the standard error of the mean is _____. a. 13.5 b. 9 c. 2.26 d. 1.5

1.5

Refer to Exhibit 8-3. 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

1.51

.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 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

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

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

117

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

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

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

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

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

2.064

The z value for a 97.8% confidence interval estimation is _____. a. 2.02 b. 1.96 c. 2.00 d. 2.29

2.29

Refer to Exhibit 8-2. 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

2.804 to 3.196

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 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

24.301 to 25.699

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

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

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 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 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

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

5

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

Refer to Exhibit 8-3. 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

57.735 to 62.265

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

69.29 to 82.71

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

7.84 or less

. 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

75

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

8.384 to 11.616

Refer to Exhibit 8-1. 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

8.74 to 9.26

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

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

CONFIDENCE.NORM

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

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.

If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

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

NORM.S.INV

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.

STDEV

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

a population parameter

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

a random sample was selected

If the margin of error in an interval estimate of μ is 4.6, the interval estimate equals _____. a. b. c. d.

answer b

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

answer d

Refer to Exhibit 8-3. 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

become wider

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

becomes narrower

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.

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.

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

becomes 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

confidence coefficient

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.

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

confidence level

As the sample size increases, the margin of error _____. a. increases b. decreases c. stays the same d. None of the answers is correct.

decreases

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

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

degrees of freedom

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

interval estimate

In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with _____ degrees of freedom. a. b. c. n − 1 d. n

n-1

As the degrees of freedom increase, the t distribution approaches the _____ distribution. a. uniform b. normal c. exponential d. p

normal

57. 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

p=0.50

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

point estimate, margin of error

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

r distribution with 24 degrees of freedom

Refer to Exhibit 8-2. 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

remains unchanged

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

sample mean

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

sample size

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

standard normal distribution

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

t distribution

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

the mean of the population

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.

the sample standard deviation and t distribution can be used

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.

the sample standard deviation is used to estimate the population standard deviation

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.

the t distribution with 49 degrees of freedom must be used

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

using a planningvalue p* closer to 0.5

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

whether there is sampling error

In general, higher confidence levels provide _____. a. wider confidence intervals b. narrower confidence intervals c. a smaller standard error d. unbiased estimates

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

width of the confidence interval to increase