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Exam 8: Confidence Intervals

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Question 31

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A random sample of electronic components had the following operational times before failure, in hours. $\begin{array} { l l l l l } \hline 322 & 350 & 346 & 347 & 335 \\\hline 323 & 341 & 355 & 329 & \\\hline\end{array}$ Assume the population standard deviation is $\sigma = 36$ and that the population is approximately normal. Construct a 90% confidence interval for the operational time before failure.

A) (318.9, 358.4)
B) (331.3, 346.1)
C) (279.4, 397.9)
D) (332.1, 345.3)

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Question 32

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The following MINITAB output presents a confidence interval for a population mean. $\begin{array} { c r r r c c } \hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 99 \% \text { CI } \\\mathrm { x } & 28 & 108.1268 & 30.4888 & 5.7618 & ( 92.161,124.093 ) \\\hline\end{array}$ Use the information in the output to construct a 98% confidence interval.

A) (92.161,124.093)
B) (105.546,110.707)
C) (93.878,122.376)
D) (105.235,111.018)

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Question 33

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The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion. Use the information in the display to construct a 95% confidence interval for p.

The following display from a TI-84 Plus calculator presents a 95% confidence interval. Fill in the blanks: We are ________ confident that the population mean is between _______ and _______.

A simple random sample of size 20 has mean $\bar { x } = 70.89$ and standard deviation s = 16.77. The population distribution is unknown. Determine the correct method of finding a 90% confidence Interval for the population mean and compute it.

A random sample of 80 adults is chosen and their mean serum cholesterol level is found to be 202 milligrams per deciliter. Assume that the population standard deviation is $\sigma = 40$ Based on a 95% confidence interval for the mean serum cholesterol, is it likely that the mean serum Cholesterol is greater than 219? (Hint: you should first construct the 95% confidence interval.)

Find the critical value $z _ { \alpha / 2 }$ needed to construct a(n) 99.3% confidence interval.

Find the confidence level for an interval which has a critical value of 1.05.

A simple random sample of size 41 has mean $\bar { x } = 70.55$ and standard deviation s = 15.73. The population distribution is unknown. Determine the correct method of finding a 90% confidence Interval for the population mean and compute it.

Find the point estimate for the given values of x and n. $x = 106 , n = 195$

In a survey of 464 registered voters, 133 of them wished to see Mayor Waffleskate lose her next election. The Waffleskate campaign claims that no more than 29% of registered voters wish to see Her defeated. Does the 98% confidence interval for the proportion support this claim? (Hint: you Should first construct the 98% confidence interval for the proportion of registered voters who wish To see Waffleskate defeated.)

The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion. Fill in the blanks: We are ________ confident that the population mean is between _______ and _______.

The following MINITAB output presents a 95% confidence interval. $\begin{array} { c c c c c } \hline { \text { The assumed sigma } = 9.4962 } & \\\\\text { Variable } & \mathrm { N } & \text { Mean } & \text { SE Mean } & 95 \% \text { CI } \\\mathrm { x } & 49 & 48.340 & 1.3566 & ( 45.681,50.999 ) \\\hline\end{array}$ Use the appropriate critical value along with the information in the computer output to construct a 99 confidence interval.

Find the critical value $z _ { \alpha / 2 }$ needed to construct a(n) 97% confidence interval.

Find the critical values for a 98% confidence interval using the chi-square distribution with 20 degrees of freedom.

Measurements were made of the milk fat content (in percent) in six brands of feta cheese (a variety of goat cheese) , with the following results. Assume that the population is normally distributed. $\begin{array} { l l l l l l } \hline 16.7 & 20.1 & 19.6 & 21.7 & 22.0 & 23.9 \\\hline\end{array}$ Construct a 90% confidence interval for the population standard deviation σ.

Boxes of raisins are labeled as containing 22 ounces. Following are the weights, in ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximately normal. $\begin{array} { l l l l l l } \hline 21.72 & 21.75 & 21.62 & 21.92 & 22.10 & 22.13 \\\hline 22.25 & 22.26 & 22.04 & 21.88 & 22.02 & 22.15 \\\hline\end{array}$ Construct a 95% confidence interval for the mean weight.

A sample of size n = 16 is drawn from an approximately normal population whose standard deviation is $\sigma = 10.5$ The sample mean is $\bar { x } = 51.0$ Construct a 99% confidence interval for $\boldsymbol { \mu }$

A sample of size n = 14 has a sample mean $\bar { x } = 11.9$ and sample standard deviation s = 2.1. It is reasonable to assume that the population is approximately normal. Construct a 99% confidence Interval for the population mean $\mu$

A simple random sample of kitchen toasters is to be taken to determine the mean operational lifetime in hours. Assume that the lifetimes are normally distributed with population standard Deviation $\sigma = 21$ hours. Find the sample size needed so that a 98% confidence interval for the mean lifetime will have a margin Of error of 4.