# Standard deviation, and Hypothesis Testing Multiple Choice

Please see the attached file.

1

If you were constructing a 99% confidence interval of the population mean based on a sample of n = 25 where the standard deviation of the sample s = 0.05, the critical value of t will be:

a.) 2.7969.

b.) 2.7874.

c.) 2.4922.

d.) 2.4851.

2

The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inch. What is the probability that a randomly selected Ping-Pong ball will have a diameter between 1.31 and 1.33 inches?

a.) 0.0987

b.) 0.1747

c.) 0.2734

d.) 0.3721

3

The width of a confidence interval estimate for a proportion will be:

a.) narrower for 99% confidence than for 95% confidence.

b.) wider for a sample size of 100 than for a sample size of 50.

c.) narrower for 90% confidence than for 95% confidence,

d.) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.

4

Assume that house prices in a neighborhood are normally distributed with standard deviation $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?

a.) 0.3174

b.) 0.1587

c.) 0, because it is assumed that the sample mean is equal to the population mean in a normally distributed population.

d.) Cannot be determined from the information given.

5

The standard error of the mean:

a.) is never larger than the standard deviation of the population,

b.) decreases as the sample size increases.

c.) measures the variability of the mean from sample to sample.

d.) all of the above.

6

Which of the following is true about the sampling distribution of the sample mean?

a.) The mean of the sampling distribution is always μ.

b.) The standard deviation of the sampling distribution is always s.

c.) The shape of the sampling distribution is always approximately normal.

d.) All of the above are true.

7

For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.

a.) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes.

b.) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.

c.) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8

minutes.

d.) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.

8

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the upper end point in a 99% confidence interval for the average income?

a.) $15,052

b.) $15,141

c.) $15,330

d.) $15,364

9

When determining the sample size necessary for estimating the true population mean, which factor is not considered when sampling with replacement?

a.) The population size

b.) The population standard deviation

c.) The level of confidence desired in the estimate

d.) The allowable or tolerable sampling error

10

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

a.) 105

b.) 150

c.) 420

d.) 597

11

The standard error of the mean for a sample of 100 is 30. In order to manipulate the standard error of the mean to be 15, we would:

a.) increase the sample size to 200.

b.) increase the sample size to 400.

c.) decrease the sample size to 50.

d.) decrease the sample size to 25.

12

A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain 's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results : L J = $50. 50 s2 and = 400. Assuming the distribution of the amount spent on their first visit is approximately normal , what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ0

a.) Approximately normal with a mean of $50.50

b.) A standard normal distribution

c.) A t distribution with 15 degrees of freedom

d.) A t distribution with 14 degrees of freedom

13

When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be, the the sample size required.

a.) smaller

b.) larger

c.) sample size is not affected

d.) the effect cannot be determined from the information given

14

A statistician wishes to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181 ,260, $5,836, 180). Which of the following interpretations is correct?

a.) 97% of the sampled total compensation values fell between $2,181,260 and $5,836,180.

b.) We are 97% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180.

c.) In the population of service industry CEOs, 97% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180.

d.) We are 97% confident that the average total compensation of all CEOs in the service industry falls in the interval $2,181,260 to $5,836,180.

15

The use of the finite population correction factor when sampling without replacement from finite populations will:

a.) increase the standard error of the mean.

b.) not affect the standard error of the mean.

c.) reduce the standard error of the mean.

d.) only affect the proportion, not the mean.

16

An internal control policy for an online fashion accessories store requires a quality assurance check before a shipment is made. The tolerable exception rate for this internal control is 0.05. During an audit, 500 shipping records were sampled from a population of 5,000 shipping records and 12 were found that violated the control. What is the upper bound for a 95% one-sided confidence interval estimate for the rate of noncompliance?

a.) 0.0060

b.) 0.0067

c.) 0.0347

d.) 0.0374

17

A stationery store wants to estimate the total retail value of the 300 greeting cards that it has in its inventory. What are the upper and lower limits of the 95% confidence interval estimate of the population total value of all greeting cards that are in inventory if a random sample of 20 greeting cards indicates an average value of $1.67 and a standard deviation of $0.32?

a.) $457.52 and $544.48

b.) $465.08 and $536.92

c.) $460.29 and $541.72

d.) $457.67 and $544.33

18

Which of the following is not true about the student's t distribution?

a.) It has more area in the tails and less in the center than does the normal distribution.

b.) It is used to construct confidence intervals for the population mean when the population standard deviation is known.

c.) It is bell-shaped and symmetrical.

d.) As the number of degrees of freedom increases, the t distribution approaches the normal distribution.

19

If the expectation of a sampling distribution is located at the parameter it is estimating, then we call that sampling distribution:

a.) unbiased.

b.) minimum variance.

c.) biased.

d.) random.

20

The personnel director of a large corporation wishes to study absenteeism among clerical workers at the corporation's central office during the year. A random sample of 25 clerical workers revealed the following:

Absenteeism : U = 9.7 days and S = 4.0 days

12 clerical workers were absent more than 10 days

What are the upper and lower limits of the 95% confidence interval estimate of the mean number

of absences for clerical workers last year

a.) 8.132 and 11.268

b.) 8.049 and 11.351

c.) 8.052 and 11.348

d.) 8.331 and 11.069

21

Why is the Central Limit Theorem so important to the study of sampling distributions?

a.) It allows us to disregard the size of the sample selected when the population is not normal.

b.) It allows us to disregard the shape of the sampling distribution when the size of the population

is large.

c.) It allows us to disregard the size of the population we are sampling from.

d.) It allows us to disregard the shape of the population when n is large.

22

Approximately 5% of U.S. families have a net worth in excess of $1 million and thus can be called "millionaires." However, a survey in the year 2000 found that 30% of Microsoft's 31,000 employees were millionaires. If random samples of 100 Microsoft employees had been taken that year, what proportion of the samples would have been between 25% and 35% millionaires?

a.) 0.1379

b.) 0.2758

c.) 0.7242

d.) 1.0911

23

A 99% confidence interval estimate can be interpreted to mean that:

a.) if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval.

b.) we have 99% confidence that we have selected a sample whose interval does include the population mean.

c.) both of the above.

d.) none of the above.

24

The fill amount of bottles of soft drink has been found to be normally distributed with a mean of 2.0 liters and a standard deviation of 0.05 liter. If a random sample of bottles is selected, what is the probability that the sample mean will be between 1.99 and 2.0 liters?

a.) 0.4772

b.) 0.5228

c.) 0.9544

d.) Cannot be determined from the information given.

25

For sample size 16, the sampling distribution of the mean will be approximately normally distributed:

a.) regardless of the shape of the population.

b.) if the shape of the population is symmetrical.

c.) if the sample standard deviation is known.

d.) if the sample is normally distributed.

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#### Solution Preview

Please see attached file for complete answers.

1 If you were constructing a 99% confidence interval of the population mean based on a sample of n

= 25 where the standard deviation of the sample s = 0.05, the critical value of t will be:

a.) 2.7969.

b.) 2.7874.

c.) 2.4922.

d.) 2.4851.

Answer: a. 2.7969

sample size=n= 25

Significance level a (alpha) = 1.00% 0r 0.01 =100%-99%

degrees of freedom=n-1= 24

No of tails= 2

t value= 2.7969 (from the tables)

corresponding to 24 degrees of freedom and 0.01 significance level

2 The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately

normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inch. What is the

probability that a randomly selected Ping-Pong ball will have a diameter between 1.31 and 1.33

inches?

a.) 0.0987

b.) 0.1747

c.) 0.2734

d.) 0.3721

Answer: b. 0.1747

Mean= M = 1.30

Standard deviation =s = 0.04

x1= 1.33

x2= 1.31

z1=(x1- M )/s = 0.75 =(1.33-1.3)/0.04

z2=(x2- M )/s = 0.25 =(1.31-1.3)/0.04

Cumulative Probability corresponding to z1= 0.75 is= 0.7734 0r= 77.34%

Cumulative Probability corresponding to z2= 0.25 is= 0.5987 0r= 59.87%

Therefore probability that the value of x will be between x1= 1.33 and x2= 1.31

is = 0.1747 =.7734-.5987

3 The width of a confidence interval estimate for a proportion will be:

a.) narrower for 99% confidence than for 95% confidence.

b.) wider for a sample size of 100 than for a sample size of 50.

c.) narrower for 90% confidence than for 95% confidence,

d.) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.

Answer: c. narrower for 90% confidence than for 95% confidence.

The more the sample size the narrower the range

The more the confidence interval the wider the range

The width does not depend on the sample proportion

4 Assume that house prices in a neighborhood are normally distributed with standard deviation

$20,000. A random sample of 16 observations is taken. What is the probability that the sample

mean differs from the population mean by more than $5,000?

a.) 0.3174

b.) 0.1587

c.) 0, because it is assumed that the sample mean is equal to the population mean in a normally

distributed population.

d.) Cannot be determined from the information given.

Answer: b.) 0.1587

Standard deviation =s = $20,000

sample size=n= 16

s x=standard error of mean=s / square root of n= $5,000 = ( 20000 / square root of 16)

z=(sample mean- M )/s x= 1 =5000/5000

Cumulative Probability corresponding to z= 1 is= 0.8413

Therefore Probability of exceeding z= 1 is 0.1587 = 1- 0.8413

5 The standard error of the mean:

a.) is never larger than the standard deviation of the population,

b.) decreases as the sample size increases.

c.) measures the variability of the mean from sample to sample.

d.) all of the above.

Answer: d.) all of the above.

standard error of mean=standard deviation/ square root of n, where n is the sample size

Thus it can never be greater than the standard deviation as square root of n is in the denominator and n is 1 or greater than 1

It decreases as n increases as square root of n is in the denominator

Standard error of mean measures the variability of the mean from sample to sample

6 Which of the following is true about the sampling distribution of the sample mean?

a.) The mean of the sampling distribution is always M .

b.) The standard deviation of the sampling distribution is always s.

c.) The shape of the sampling distribution is always approximately normal.

d.) All of the above are true.

Answer: a.) The mean of the sampling distribution is always M .

The standard deviation of the sampling distribution is s/ square root of n where n is the sample size

The shape of the sampling distribution is approximately normal only when the sample size is large

7 For air travelers, one of the biggest complaints is of the waiting time between when the airplane

taxis away from the terminal until the flight takes off. This waiting time is known to have a

skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes.

Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean

waiting time between when the airplane taxis away from the terminal until the flight takes off for

these 100 flights.

a.) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes.

b.) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.

c.) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8

minutes.

d.) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.

Answer:

c. Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.

The sampling distribution of the mean approaches a normal distribution as n increases, even if the underlying population distribution is far from normal.

Standard deviation =s = 8 min

sample size=n= 100

s x=standard error of mean=s / square root of n= 0.8 = ( 8 / square root of 100)

8 An economist is interested in studying the incomes of consumers in a particular region. The

population ...

#### Solution Summary

Answers to 25 Multiple choice questions on Standard deviation, Hypothesis testing and other statistics concepts