Confidence Intervals for a Population Mean

Confidence intervals for the mean mu

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Question 1

Question 1.

What is the purpose of a 90% confidence interval?

To give a range of values for the data

To estimate the value of µ with an intervals of reasonable values

To tell us the level of confidence

Incorrect. A confidence interval is an estimate of a parameter in interval form with associated confidence.

Correct. A confidence interval is an estimate of a parameter in interval form with associated confidence.

Incorrect. Try again.

Question 2

170

Question 2.

If $ \overline{x} $ = 7.5 hours and margin of error = 0.33 hours for 95% confidence. What is the 95% confidence interval for µ?

(-12.5, 27.5)

Cannot be determined based on information given.

(7.17, 7.83)

Incorrect. (

- ME,

+ ME) or (7.5 - 0.33, 7.5 + 0.33) or (7.17, 7.83).

$\overline{x}$ $\overline{x}$

Correct. (

- ME,

+ ME) or (7.5 - 0.33, 7.5 + 0.33) or (7.17, 7.83).

$\overline{x}$ $\overline{x}$

Incorrect. Try again.

Question 3

382

Question 3.

A 95% confidence interval estimate for the average lifetime of Duracell batteries is (7.17, 7.83). Which of the following gives a correct interpretation of this interval?

We are 95% confident that the average lifetime of all Duracell batteries is between 7.17 and 7.83 hours.

We are 95% confident that the lifetimes of all Duracell batteries are between 7.17 and 7.83 hours

The probability is 0.95 that the average lifetime of all Duracell batteries is between 7.17 and 7.83 hours.

Incorrect. A 95% confidence interval for µ gives us a range of feasible values for µ. Thus, we are 95% confident that the value of µ (the average lifetime of all Duracell batteries) is between 7.17 and 7.83 hours.

Correct. A 95% confidence interval for µ gives us a range of feasible values for µ. Thus, we are 95% confident that the value of µ (the average lifetime of all Duracell batteries) is between 7.17 and 7.83 hours.

Incorrect. Try again.

Question 4

547

Question 4.

What is the formula for margin of error for estimating µ with a confidence interval?

$ z^{*} \frac{ \sigma} { \sqrt{n}} $

$ \frac{ \sigma} { \sqrt{n}} $

$ z^{*} \frac{ 1} { \sqrt{n}} $

Incorrect.

is the formula for margin of error.

$z^{*} \frac{ \sigma} { \sqrt{n}}$

Correct.

is the formula for margin of error.

$z^{*} \frac{ \sigma} { \sqrt{n}}$

Incorrect. Try again.

Question 5

704

Question 5.

What is the value of z* for 98% confidence?

1.960

2.326

1.645

2.576

Incorrect. According to the chart, z* for 98% confidence is 2.326.

Correct. According to the chart, z* for 98% confidence is 2.326.

Incorrect. Try again.

Question 6

768

Question 6.

What parameter do the researchers want to estimate with a 95% confidence interval?

95% of the hemoglobin levels for all breast fed infants

The level of confidence

The mean hemoglobin level for all breast fed infants

The mean hemoglobin level for the sample of 26 breast fed infants

Incorrect. The researchers want to estimate "the mean hemoglobin level of all breast fed infants."

Correct. The researchers want to estimate "the mean hemoglobin level of all breast fed infants."

Incorrect. Try again.

Question 7

812

Question 7.

Why did we need to plot the 26 hemoglobin levels?

To estimate the variability in the sample of hemoglobin levels.

To make sure there are no outliers indicating non-Normality.

To find the sample mean, $\overline{x} $.

Incorrect. Outliers indicate non-Normality. Since one of the conditions is Normality of the hemoglobin levels, we plot the hemoglobin levels to make sure we don't have non-Normality.

Correct. Outliers indicate non-Normality. Since one of the conditions is Normality of the hemoglobin levels, we plot the hemoglobin levels to make sure we don't have non-Normality.

Incorrect. Try again.

Question 8

842

Question 8.

What is the value of z* for 95% confidence?

2.576

2.326

1.645

1.960

Incorrect. According to the z* row of Table C, z* for 95% confidence is 1.960.

Correct. According to the z* row of Table C, z* for 95% confidence is 1.960.

Incorrect. Try again.

Question 9

920

Question 9.

What is the name of the value 0.62?

Margin of error

Estimate of µ

Level of confidence

Incorrect. We add and subtract margin of error from

= 12.9.

$\overline{x}$

Correct. We add and subtract margin of error from

= 12.9.

$\overline{x}$

Incorrect. Try again.

Question 10

977

Question 10.

What parameter do the students want to estimate with a 90% confidence interval?

95% of the number of months students dated before becoming engaged for all married students at this university

The mean number of months students dated before becoming engaged for all married students at this university

The level of confidence

The mean number of months students dated before becoming engaged for the sample of 121 married students at this university

Incorrect. The students want to estimate "the mean number of months students dated before becoming engaged."

Correct. The students want to estimate "the mean number of months students dated before becoming engaged."

Incorrect. Try again.

Question 11

1049

Question 11.

The plot of the data clearly indicates outliers. Why is the resulting confidence interval still valid?

Because the sample size of 121 is large enough to apply the Central Limit Theorem.

Because there are several outliers, not just one.

Because the standard deviation of 10 is greater than the sample mean $\overline{x} $ of 9.34.

Incorrect. When the sample is large and random, we can apply the Central Limit Theorem and know that the sampling distribution of

is approximately Normal.

$\overline{x}$

Correct. When the sample is large and random, we can apply the Central Limit Theorem and know that the sampling distribution of

is approximately Normal.

$\overline{x}$

Incorrect. Try again.

Question 12

1067

Question 12.

What is the value of z* for 90% confidence?

2.326

1.960

1.645

2.576

Incorrect. According to the z* row of Table C, z* for 90% confidence is 1.645.

Correct. According to the z* row of Table C, z* for 90% confidence is 1.645.

Incorrect. Try again.

Question 13

1076

Question 13.

What is the name of the value 1.50?

Level of confidence

Margin of error

Estimate of µ

Incorrect. We add and subtract margin of error from

= 9.34.

$\overline{x}$

Correct. We add and subtract margin of error from

= 9.34.

$\overline{x}$

Incorrect. Try again.

Question 14

1128

Question 14.

True or false: The interpretation of the interval (7.84, 10.84) is correctly given in terms of confidence and not probability.

True

False

Incorrect. Saying "We are approximately 90% confident that . . ." correctly gives the interpretation in terms of confidence rather than probability.

Correct. Saying "We are approximately 90% confident that . . ." correctly gives the interpretation in terms of confidence rather than probability.

Incorrect. Try again.

Questions 15-16

1249

Question 15.

True or false: A correct interpretation of a confidence interval must state the parameter correctly in context.

False

True

Incorrect. Since a confidence interval is an estimate of a parameter, a correct interpretation needs to state this parameter.

Correct. Since a confidence interval is an estimate of a parameter, a correct interpretation needs to state this parameter.

Incorrect. Try again.

Questions 17-18

1326

Question 17.

Do all three of these interpretations give "confidence" rather than "probability?"

Yes

Incorrect. All three of these interpretations correctly report "confidence" rather than "probability."

Correct. All three of these interpretations correctly report "confidence" rather than "probability."

Incorrect. Try again.

Questions 19-21

1644

Question 19.

Does the confidence interval interpretation, "99% of the IQs are contained in the interval (95.3, 109.2)," state the parameter in context?

Yes

Incorrect. The parameter is "the mean IQ" and it is not stated in the interpretation. This confidence interval gives reasonable values for "the mean IQ," not a range of values for the "IQs."

Correct. The parameter is "the mean IQ" and it is not stated in the interpretation. This confidence interval gives reasonable values for "the mean IQ," not a range of values for the "IQs."

Incorrect. Try again.

StatTutor Lesson - Confidence Intervals for a Population Mean

Question 1

Question 1.

Question 2

Question 2.

Question 3

Question 3.

Question 4

Question 4.

Question 5

Question 5.

Question 6

Question 6.

Question 7

Question 7.

Question 8

Question 8.

Question 9

Question 9.

Question 10

Question 10.

Question 11

Question 11.

Question 12

Question 12.

Question 13

Question 13.

Question 14

Question 14.

Questions 15-16

Question 15.

Question 16.

Questions 17-18

Question 17.

Question 18.

Questions 19-21

Question 19.

Question 20.

Question 21.