Statistic 3

The standard error of the mean

Question 1 answers

is never larger than the standard deviation of the population.

decreases as the sample size increases.

measures the variability of the mean from sample to sample.

All of the above.

Question 2 text Question 2 4 points Save

Which of the following is true regarding the sampling distribution of the mean with a large sample size?

Question 2 answers

It has the same shape, mean, and standard deviation as the population.

It has a normal distribution with the same mean and standard deviation as the population.

It has the same shape and mean as the population, but has a smaller standard deviation.

It has a normal distribution with the same mean equal to the population and the standard error of the mean sigmaXbar.

Question 3 text Question 3 4 points Save

The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 71.

Question 3 answers

0.0228

0.0124

0.2135

0.1248

Question 4 text Question 4 4 points Save

The standard error of the population proportion will become larger

Question 4 answers

as population proportion approaches 0.

as population proportion approaches 0.50.

as population proportion approaches 1.00.

as the sample size increases.

Question 5 text Question 5 4 points Save

Suppose the ages of students in Statistics 101 follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is INCORRECT?

Question 5 answers

The mean of the sampling distribution is equal to 23 years.

The standard deviation of the sampling distribution is equal to 3 years.

The shape of the sampling distribution is approximately normal.

The standard error of the sampling distribution is equal to 0.3 years.

Question 6 text Question 6 4 points Save

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

Question 6 answers

18.750

2.500

1.875

0.750

Question 7 text Question 7 4 points Save

If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4 and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between $14 and $16.

Question 7 answers

True

False

Question 8 text Question 8 4 points Save

Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1 million.

Question 8 answers

Approximately 0

0.2357

0.7357

Approximately 1

Question 9 text Question 9 4 points Save

It is desired 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?

Question 9 answers

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

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

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

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.

Question 10 text Question 10 4 points Save

A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 time is 4.52 seconds to 5.18 seconds.

Question 10 answers

True

False

Question 11 text Question 11 4 points Save

A librarian asked his assistant for an estimate of the mean number of books checked out each day. The assistant estimated from 740 to 920 books per day. What is an efficient, unbiased point estimate of the number of books checked out each day?

Question 11 answers

740

830

920

None of the above.

Question 12 text Question 12 4 points Save

Which of the following is NOT true about the Student's t distribution?

Question 12 answers

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

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

It is bell shaped and symmetrical.

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

Question 13 text Question 13 4 points Save

The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

Question 13 answers

True

False

Question 14 text Question 14 4 points Save

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

Question 14 answers

narrower for 99% confidence than for 95% confidence.

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

narrower for 90% confidence than for 95% confidence.

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

Question 15 text Question 15 4 points Save

A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?

Question 15 answers

No, and we are 90% sure of it.

No. The proportion is 54.17%.

Maybe. 0.60 is a believable value of the population proportion based on the information above.

Yes, and we are 90% sure of it.

Question 16 text Question 16 4 points Save

As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, the sample mean= 9.8 and the sample variance=25. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what size sample should she choose?

Question 16 answers

n = 482

n = 166

n = 154

n = 123

Question 17 text Question 17 4 points Save

We have created a 95% confidence interval for μ (mu) with the result (10, 15). What decision will we make if we test H0: μ = 16 versus H1: μ ≠ 16, at α = .05?

Question 17 answers

Reject H0

Accept H0

Fail to reject H0

Cannot tell what the decision ought to be from the information given.

Question 18 text Question 18 4 points Save

A Type I error is committed when

Question 18 answers

we reject a null hypothesis that is true.

we don't reject a null hypothesis that is true.

we reject a null hypothesis that is false.

we do not reject a null hypothesis that is false.

Question 19 text Question 19 4 points Save

Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: Xbar (the sample mean) = 52, and s (the sample standard deviation) = 22. Also, assume this test statistic falls in the rejection region at α = .05. Which of the following decision is correct?

Question 19 answers

At α = 0.05, we do not reject H0.

At α = 0.05, we reject H0.

At α = 0.05, we believe H0.

At α = 0.10, we do not reject H0.

Question 20 text Question 20 4 points Save

A Type II error is committed when

Question 20 answers

we reject a null hypothesis that is true.

we don't reject a null hypothesis that is true.

we reject a null hypothesis that is false.

we do not reject a null hypothesis that is false.

Question 21 text Question 21 4 points Save

If a test of hypothesis has a Type I error probability, α = 0.01, we mean

Question 21 answers

If the null hypothesis is true, we do not reject it 1% of the time.

If the null hypothesis is true, we reject it 1% of the time.

If the null hypothesis is false, we do not reject it 1% of the time.

if the null hypothesis is false, we reject it 1% of the time.

Question 22 text Question 22 4 points Save

Which of the following would be an appropriate alternative hypothesis?

Question 22 answers

The population proportion is less than 0.65.

The sample proportion is less than 0.65.

The population proportion is not less than 0.65.

The sample proportion is not less than 0.65.

Question 23 text Question 23 4 points Save

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. Pick the appropriate hypotheses. (Note that Xbar is the sample mean.)

Question 23 answers

H0: μ ≥ 30 H1: μ < 30

H0: μ ≤ 30 H1: μ > 30

H0: Xbar ≥ 30 H1: Xbar < 30

H0: Xbar ≤ 30 H1: Xbar > 30

Question 24 text Question 24 4 points Save

For a given level of significance, if the sample size is increased, the power of the test will increase.

Question 24 answers

True

False

Question 25 text Question 25 4 points Save

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.

Question 25 answers

True

False