Final Exam Review 2

Time spent by office workers using email per session is normally distributed with a mean, µ, of 8 minutes and a standard deviation, σ, of 2 minutes. A random sample of 25 workers was selected. What is the standard error of the mean?

0.4

A student researcher is interested in estimating the time taken by UNCW students to walk from Kenan Auditorium to the Congdon Hall. A random sample of 24 students were selected and the time taken by them to walk between the buildings was measured. Their sample mean time was 12.3 minutes with a standard deviation of 3.2 minutes. The 99% confidence interval (rounded to two decimals) is:

(10.47, 14.13)

If the sample mean is 15 and the margin of error is 3, what is the range of the confidence interval?

(12, 18) (15-3, 15+3)

A corporation that owns apartment complexes wishes to estimate the average length of time residents remain in the same apartment before moving out. A sample of 150 rental contracts gave a mean length of occupancy of 3.7 years with a population standard deviation of 1.2 years. Construct a 95% confidence interval for the mean length of occupancy of apartments owned by this corporation. For this problem, what is the confidence interval?

(3.51, 3.89) - sample mean +/- MoE

A survey of hospital records for 25 randomly selected patients suffering from a particular disease indicated that the average hospital stay was 10 days with a standard deviation of 2.1 days. Find a 99% confidence interval for the mean number of days all sufferers of this disease spend in the hospital. What is the 99% confidence interval?

(8.83, 11.17)

A survey of hospital records for 25 randomly selected patients suffering from a particular disease indicated that the average hospital stay was 10 days with a standard deviation of 2.1 days. Find a 99% confidence interval for the mean number of days all sufferers of this disease spend in the hospital. What is the new confidence interval with the new sample?

(8.88, 11.12)

Suppose that the average number of "friends" that social media users have is normally distributed with a mean of 130 and a standard deviation of about 50. Twenty-five social media users are randomly chosen. For this sample of 25, what is the probability that the average number of "friends" is greater than 145? What is the Z score corresponding to 145?

+ 1.5

Let sigma be unknown. If the sample size in a problem is 25 and confidence level is 99%, which column will you go to in the T table?

0.005

Suppose that the average number of "friends" that social media users have is normally distributed with a mean of 130 and a standard deviation of about 50. Twenty-five social media users are randomly chosen. For this sample of 25, what is the probability that the average number of "friends" is greater than 145? Using the Z table, what is the probability that for the sample of 25, the average number of "friends" is over 145?

0.0668

A corporation that owns apartment complexes wishes to estimate the average length of time residents remain in the same apartment before moving out. A sample of 150 rental contracts gave a mean length of occupancy of 3.7 years with a population standard deviation of 1.2 years. Construct a 95% confidence interval for the mean length of occupancy of apartments owned by this corporation. For this problem, what is the standard error of the mean?

0.098

Time spent by office workers using email per session is normally distributed with a mean, µ, of 8 minutes and a standard deviation, σ, of 2 minutes. A random sample of 25 workers was selected. What is the probability that the average time spent reading email for this sample is less than 7.5 minutes?

0.1056

A corporation that owns apartment complexes wishes to estimate the average length of time residents remain in the same apartment before moving out. A sample of 150 rental contracts gave a mean length of occupancy of 3.7 years with a population standard deviation of 1.2 years. Construct a 95% confidence interval for the mean length of occupancy of apartments owned by this corporation. For this problem, what is the margin of error?

0.1921

In hypothesis testing, after evaluating errors in a hypothesis test, you conclude that the Type I error is very serious and much more serious than a Type II error. Which of these would be the best alpha level (significance level) for your test?

α = 0.01 (Since alpha is the probability of a Type I error, you want it to be as low as possible if that error is very serious.)

x̅ is the point estimator for

μ

The symbol use to represent the mean of the sampling distribution is

μx̅

The Standard Error of the Mean is given by

σ/sqrt(n)

The critical value to construct a 95% confidence interval with σ unknown for a sample of size 4 is

3.182

The confidence level in a hypothesis test is indicated by the symbol

1 - α

A survey of hospital records for 25 randomly selected patients suffering from a particular disease indicated that the average hospital stay was 10 days with a standard deviation of 2.1 days. Find a 99% confidence interval for the mean number of days all sufferers of this disease spend in the hospital. What is the margin of error for the problem?

1.1747

What is the Z critical value for a 90% confidence interval?

1.645

A student researcher is interested in estimating the time taken by UNCW students to walk from Kenan Auditorium to the Congdon Hall. A random sample of 24 students were selected and the time taken by them to walk between the buildings was measured. Their sample mean time was 12.3 minutes with a standard deviation of 3.2 minutes. For a 99% confidence interval, the margin of error is:

1.8336

A corporation that owns apartment complexes wishes to estimate the average length of time residents remain in the same apartment before moving out. A sample of 150 rental contracts gave a mean length of occupancy of 3.7 years with a population standard deviation of 1.2 years. Construct a 95% confidence interval for the mean length of occupancy of apartments owned by this corporation. For this problem, what is the critical value?

1.96

A software engineer wishes to estimate, to within 5 seconds, the mean time that a new application takes to start up, with 95% confidence. Estimate the minimum size sample required if the standard deviation of start up times for similar software is 12 seconds. What is the critical value for this study?

1.96

Let sigma be unknown. If the sample size is 45, and confidence level is 95%, what is the critical value from the t-table?

1.960

Suppose that the average number of "friends" that social media users have is normally distributed with a mean of 130 and a standard deviation of about 50. Twenty-five social media users are randomly chosen. For this sample of 25, what is the probability that the average number of "friends" is greater than 145? What is the standard error of the mean?

10

In hypothesis testing, if the confidence level of a test is 90%, the significance level would be

10% (from the table, significance level + confidence level = 100%)

Which one of the following is NOT an acceptable confidence level?

100%

Suppose that the average number of "friends" that social media users have is normally distributed with a mean of 130 and a standard deviation of about 50. Twenty-five social media users are randomly chosen. For this sample of 25, what is the probability that the average number of "friends" is greater than 145? What is the mean of the sampling distribution?

130

Let sigma be unknown. If the sample size is 17 and the confidence level is 95%, what is the critical value?

2.12

If sigma is unknown, and if the sample size in a problem is 4, for a confidence level of 90%, what is the t-critical value?

2.353

A survey of hospital records for 25 randomly selected patients suffering from a particular disease indicated that the average hospital stay was 10 days with a standard deviation of 2.1 days. Find a 99% confidence interval for the mean number of days all sufferers of this disease spend in the hospital. What is the critical value for this problem?

2.797

A software engineer wishes to estimate, to within 5 seconds, the mean time that a new application takes to start up, with 95% confidence. Estimate the minimum size sample required if the standard deviation of start up times for similar software is 12 seconds. What is the minimum sample size needed to conduct this study using the engineer's specifications?

23

A tax assessor wants to assess the mean property tax bill for all homeowners in Madison, Wisconsin to within $100 with 90% confidence. A survey ten years ago got an estimate of the standard deviation to be $1000. What is the minimum sample size needed for this study?

271

A software engineer wishes to estimate, to within 5 seconds, the mean time that a new application takes to start up, with 95% confidence. Estimate the minimum size sample required if the standard deviation of start up times for similar software is 12 seconds. What is the Margin of Error for this study?

5 seconds

You are given that a 99% confidence interval for a population mean is (12, 28). The margin of error used to construct this confidence interval was

8 (The sample mean is 20. The margin of error is +/- 8 to get to the bounds of the interval from the center.)

What is the margin of error for a 90% confidence interval?

About 1.645 Standard Errors

What is the margin of error for a 95% confidence interval?

About 1.96 Standard Errors

What are Confidence Intervals?

Confidence Intervals provide a range of values to estimate a population parameter

T or F: If we take many samples from a population and calculate the sample means, all of the sample means will always be the same.

False

T or F: The sampling distribution is the same as the population distribution.

False

The administrator at your local hospital states that on weekends the average wait time for emergency room visits is 10 minutes. Based on discussions you have had with friends who have complained about how long they waited to be seen in the ER over a weekend, you believe that the wait time is higher. The null and alternative hypotheses for this test are:

H0: µ ≤ 10 and Ha: µ > 10

A software engineer wishes to estimate, to within 5 seconds, the mean time that a new application takes to start up, with 95% confidence. Estimate the minimum size sample required if the standard deviation of start up times for similar software is 12 seconds. If the engineer wants to estimate the average time to within 2 seconds what will happen to his required minimum sample size?

It will increase to more than 23

Let sigma be unknown. If the sample size in a problem is 25 and confidence level is 99%, which row will you go to in the T table?

Row 24 (25-1)

What does the symbol 1 - a represent?

The confidence level expressed as a decimal

The Margin of Error is

a multiple of the standard error

The type of test to be performed here is

a one-tailed test

As the confidence level increases, the Margin of Error

also increases

A hypothesis test was conducted to see if a new vaccine reduces the risk of contracting a certain virus. The researchers believe that the new vaccine will be effective. Their null and alternative hypotheses are: Ho: the vaccine is not effective against the virus and Ha: the new vaccine is effective against the virus. What is the Type I error here?

concluding that the new vaccine is effective when it really is not

As the sample size increases, the standard error of the mean

decreases

In hypothesis testing, as α increases, what happens to β ?

decreases

The null hypothesis usually represents:

existing beliefs about the population

A corporation that owns apartment complexes wishes to estimate the average length of time residents remain in the same apartment before moving out. A sample of 150 rental contracts gave a mean length of occupancy of 3.7 years with a population standard deviation of 1.2 years. Construct a 95% confidence interval for the mean length of occupancy of apartments owned by this corporation. If we change the confidence level to 98% while keeping all else constant, what happens to the confidence interval?

gets wider

A researcher asserts that he has proved both the null and the alternative hypothesis. What can we say?

he is lying, this is not possible

A corporation that owns apartment complexes wishes to estimate the average length of time residents remain in the same apartment before moving out. A sample of 150 rental contracts gave a mean length of occupancy of 3.7 years with a population standard deviation of 1.2 years. Construct a 95% confidence interval for the mean length of occupancy of apartments owned by this corporation. If we want to retain a confidence level of 95% but get a narrower, more precise confidence interval, what can we do?

increase sample size

A student researcher is interested in estimating the time taken by UNCW students to walk from Kenan Auditorium to the Congdon Hall. A random sample of 24 students were selected and the time taken by them to walk between the buildings was measured. Their sample mean time was 12.3 minutes with a standard deviation of 3.2 minutes. The researcher wants to keep the same confidence level but reduce the margin of error. What can he do?

increase sample size

According to the Central Limit Theorem, the mean of the sampling distribution of sample means

is exactly the same as the population mean

All else being the same, as the sample size n increases, what happens to the margin of error?

it decreases

A tax assessor wants to assess the mean property tax bill for all homeowners in Madison, Wisconsin to within $100 with 90% confidence. A survey ten years ago got an estimate of the standard deviation to be $1000. Keeping all else the same, if there is a larger variation among tax bills in the population of homeowners, what happens to the minimum sample size required?

it increases

A student researcher is interested in estimating the time taken by UNCW students to walk from Kenan Auditorium to the Congdon Hall. A random sample of 24 students were selected and the time taken by them to walk between the buildings was measured. Their sample mean time was 12.3 minutes with a standard deviation of 3.2 minutes. All else being the same, if the confidence level is decreased, what happens to the standard error in the problem?

it remains unchanged

Suppose that a population is normally distributed. If all samples of size 5 are taken from this population, what can we say about the sampling distribution of sample means?

it will be normally distributed

According to the Central Limit Theorem, if we have a positively skewed population, and we draw all samples of size 67 from this population, what shape will the sampling distribution of sample means be?

normal

Numbers that summarize data from an entire population are called

parameters

Sampling error is defined to be the

positive difference between a sample statistic and the corresponding population parameter

The power of a hypothesis test is the probability of

rejecting the null when the alternative is true

Taking repeated samples of a given size, finding each sample mean, and then plotting the distribution of all the sample means produces a:

sampling distribution

One way to make the standard error of the mean smaller is to

take a larger sample

In hypothesis testing, what is the hypothesis that the researcher is trying to prove?

the alternative hypothesis

A survey of hospital records for 25 randomly selected patients suffering from a particular disease indicated that the average hospital stay was 10 days with a standard deviation of 2.1 days. Find a 99% confidence interval for the mean number of days all sufferers of this disease spend in the hospital. The hospital then got access to two more patient records, taking the sample size up to 27. Assume that the sample mean and sample standard deviation of the new sample does not change. What then changes in the computation of the confidence interval?

the critical value and the standard error

margin of error

the critical value times the standard error

A sampling distribution for a sample mean is

the distribution of sample means from all possible samples of a certain size

In hypothesis testing, which hypothesis is considered the default or "status quo"?

the null hypothesis

Out of the following, which quantity does the Margin of Error NOT depend on?

the sample mean

Which one of these quantities are NOT needed to determine the sample size for a study that you propose to conduct?

the sample mean

The Standard Error of the Mean is

the standard deviation of a sampling distribution of sample means

The symbol 𝜎𝑥̅ represents

the standard error of the mean

How does a t-distribution with 5 degrees of freedom compare to a T-distribution with 10 degrees of freedom?

the t-distribution with 5 degrees of freedom is flatter with thicker tails

What is the goal of interval estimation?

to estimate an unknown population parameter

Consider a population that is negatively skewed. If we take all samples of size 47 from this population, the sampling distribution of sample means

will be normally distributed

If you want to be more confident

your confidence interval (range) becomes wider