Chapter 1. Confidence Intervals for a Population Mean

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.

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2

Incorrect. (\( \overline{x} \) - ME, \( \overline{x} \) + ME) or (7.5 - 0.33, 7.5 + 0.33) or (7.17, 7.83).

Correct. (\( \overline{x} \) - ME, \( \overline{x} \) + ME) or (7.5 - 0.33, 7.5 + 0.33) or (7.17, 7.83).

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2

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.

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2

Incorrect. \( z^{*} \frac{ \sigma} { \sqrt{n}} \) is the formula for margin of error.

Correct. \( z^{*} \frac{ \sigma} { \sqrt{n}} \) is the formula for margin of error.

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2

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

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

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2

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."

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2

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.

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2

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.

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2

Incorrect. We add and subtract margin of error from \(\overline{x} \) = 12.9.

Correct. We add and subtract margin of error from \(\overline{x} \) = 12.9.

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2

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."

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2

Incorrect. When the sample is large and random, we can apply the Central Limit Theorem and know that the sampling distribution of \(\overline{x} \) is approximately Normal.

Correct. When the sample is large and random, we can apply the Central Limit Theorem and know that the sampling distribution of \(\overline{x} \) is approximately Normal.

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2

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.

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2

Incorrect. We add and subtract margin of error from \(\overline{x} \) = 9.34.

Correct. We add and subtract margin of error from \(\overline{x} \) = 9.34.

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2

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.

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2

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.

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2

Incorrect. A correct interpretation of a confidence interval gives "confidence" not "probability."

Correct. A correct interpretation of a confidence interval gives "confidence" not "probability."

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2

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

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

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2

Incorrect. The first intepretation gives the parameter as "the true mean yield in bushels per acre." The second gives the parameter as "the average angle of deformity for all patients having HAV." And the third gives the parameter as "the mean IQ of all seventh-grade girls in the school district." All give the parameter in terms of the mean response of all individuals in the population.

Correct. The first intepretation gives the parameter as "the true mean yield in bushels per acre." The second gives the parameter as "the average angle of deformity for all patients having HAV." And the third gives the parameter as "the mean IQ of all seventh-grade girls in the school district." All give the parameter in terms of the mean response of all individuals in the population.

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2

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."

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2

Incorrect. Since the interpretation states that "the sample average..." is contained in the interval, it is saying that the statistic value, not the parameter value, is contained in the interval.

Correct. Since the interpretation states that "the sample average..." is contained in the interval, it is saying that the statistic value, not the parameter value, is contained in the interval.

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2

Incorrect. "99% of the time" is not a correct statement of confidence.

Correct. "99% of the time" is not a correct statement of confidence.

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2