Quiz about Confidence Intervals and Hypothesis Testing

Question 1

What is the primary purpose of a confidence interval for a mean?

Accepted Answer

to estimate a population mean

Answer

to estimate a sample mean

Answer

to test a hypothesis about a sample mean

Answer

to provide an interval that covers 95% of the individual values in the population

Question 2

The value of z selected for constructing a confidence interval is called the ______________ value.

Accepted Answer

critical

Answer

error

Answer

confidence

Answer

student

Question 3

The sample mean , $$\overline{x}$$ is called a _______________ of the population mean $$\mu$$ ?

Accepted Answer

Point estimate

Answer

Margin of error

Answer

Standard Error

Answer

Confidence Interval

Question 4

What is the critical z-value for an 85% confidence interval?

Accepted Answer

1.44

Answer

0.8023

Answer

1.04

Answer

2.3

Question 5

Find the Critical Value for an 86% Confidence Level.

Accepted Answer

1.48

Answer

1.53

Answer

1.282

Answer

2.11

Question 6

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the critical value.

What is the point estimate?

Accepted Answer

105.2

Answer

75

Answer

10

Answer

0.90

Question 7

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the critical value.

Accepted Answer

1.645

Answer

0.90

Answer

1.155

Answer

1.283

Question 8

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the critical value.

Find the Standard Error.

Accepted Answer

1.155

Answer

75

Answer

10

Answer

105.2

Question 9

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the critical value.

Find the Margin of Error to two decimal places.

Accepted Answer

1.90

Answer

1.89

Answer

1.899

Answer

1.99

Question 10

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

Accepted Answer

(112.8, 127.4)

Answer

(114.5, 125.6)

Answer

(112.82, 127.38)

Answer

(114.56, 125.64)

Question 11

Given the Critical Value of Z = 2.11, find the Confidence Level.

Accepted Answer

96.52%

Answer

0.9652

Answer

.9826

Answer

98.26%

Question 12

A person selects a random sample of 15 credit cards and determines the annual interest rate, in percent, of each one. The sample mean is 12.42 with a sample standard deviation of 1.3. It is desired to construct a 90% Confidence Interval.

Find the Standard Error to three decimal places.

Accepted Answer

0.336

Answer

0.33566

Answer

13.156

Answer

0.087

Question 13

You are given two sets of data measuring the same information, both with the same sample size. Set A has a larger Standard Error than Set B. If you were looking for a 99.8% Confidence Interval, which set would have a larger Margin of Error?

Accepted Answer

Set A

Answer

Set B

Answer

Not enough information

Answer

I have no idea what you're asking me to do

Question 14

True or False:

The more confident you want to be, the smaller your confidence interval will be.

Accepted Answer

False

Answer

True

Question 15

True or False:

The larger your confidence interval is, the more sure (higher confidence level) you can be.

Accepted Answer

True

Answer

False

Question 16

In general, how does doubling the sample size change the confidence interval size?

Accepted Answer

Divides the interval size by 1.414

Answer

Doubles the interval size

Answer

Halves the interval size

Answer

Multiplies the interval size by 1.414

Answer

This cannot be determined without knowing the sample size

Question 17

In a simple random sample of 80 teenagers, the average number of texts handled in a day was 50 with a standard deviation of 15. What is the 96% confidence interval for the average number of texts handled by all teens daily?

Accepted Answer

$$50\pm2.088\left(\frac{15}{\sqrt{80}}\right)$$

Answer

$$50\pm2.054\left(15\right)$$

Answer

$$50\pm2.054\left(\frac{15}{\sqrt{79}}\right)$$

Answer

$$50\pm2.054\left(\frac{15}{\sqrt{80}}\right)$$

Answer

$$50\pm2.088\left(\frac{15}{\sqrt{79}}\right)$$

Question 18

The standard deviation of SAT scores is 100 points. A researcher decides to take a sample of 500 students' scores to estimate the mean score of students in your state. What is the standard deviation of the sample mean?

Accepted Answer

4.47

Answer

0.2

Answer

5

Answer

100

Answer

Cannot be determined

Question 19

You have a table of standard normal probabilities that gives you the area of the curve from the left tail to the z-score of interest. When using this type of table, what area of the curve would you use to find the corresponding z-score for confidence interval of 95%?

Accepted Answer

.05

Answer

.90

Answer

.95

Answer

.975

Answer

.475

Question 20

A teacher administers a standardized math test to his class of 75 students. The mean score (out of 300 possible points) is 235. From previous studies, you know the population standard deviation is 28. Using the sample data given, calculate a 95% confidence interval for the population mean.

Accepted Answer

(228.7, 241.3)

Answer

(234.1, 235.9)

Answer

(226.7, 243.3)

Answer

(233.0, 237.0)

Answer

(200.0, 300.0)

Question 21

According to the central limit theorem, what is the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

The standard deviation of the population divided by the square root of the sample size

Answer

The standard deviation of the population

Answer

The standard deviation of the sample

Answer

The standard deviation of the sample divided by the square root of the sample size

Question 22

Suppose the average weight for adult males (age 18 or older) in Alachua County is 190 lbs with a standard deviation of 20. Now suppose we take a random sample of 143 adult males (age 18 or older) in Alachua County. What is the probability that the average weight of our 143 subjects is bigger than 193 lbs?

Accepted Answer

.0367

Answer

.4404

Answer

.5596

Answer

.2743

Answer

.7257

Question 23

On November 1, 2017 the Gallup polling organization reported that a 95% confidence interval for the true proportion of U.S. adults in favor of the way Donald Trump is handling his job as president is (0.35, 0.41). Which of the following is the margin of error for this confidence interval?

Accepted Answer

.03

Answer

.06

Answer

.38

Answer

1.96

Question 24

Suppose that we found that a 99% confidence interval for the mean number of hours that Clemson students watch television per day was 1.67 hours to 2.52 hours. Which of the following is a correct interpretation of this result?

Accepted Answer

We are 99% confident that the true mean amount of time that Clemson students spend watching television per day is between 1.67 hours and 2.52 hours.

Answer

We can be confident that 99% of all Clemson students watch between 1.67 hours and 2.52 hours of television per day.

Answer

The probability is 0.99 that the mean number of hours that Clemson students watch television per day is between 1.67 hours and 2.52 hours.

Answer

99% of the time, a Clemson student will watch between 1.67 hours and 2.52 hours of television per day.

Confidence Intervals and Hypothesis Testing

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