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Exam 9: Estimating the Value of a Parameter Using Confidence Intervals

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Question 41

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State the Properties of Student s t-Distribution -A computer package was used to generate the following printout for estimating the sale price of condominiums in a particular neighborhood. A friend suggests that the mean sale price of homes in this neighborhood is $\$ 49,000$ . Comment on your friend's suggestion.

A) Based on this printout, all you can say is that the mean sale price might be $\$ 49,000$ .
B) Your friend is wrong, and you are $95 \%$ certain.
C) Your friend is correct, and you are $95 \%$ certain.
D) Your friend is correct, and you are $100 \%$ certain.

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Question 42

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Provide an appropriate response. -In a random sample of 60 dog owners enrolled in obedience training, it was determined that the mean amount of money spent per owner was $\$ 109.33$ per class. Assuming the population standard deviation of the amount spent per owner is $\$ 12$ , construct and interpret a $95 \%$ confidence interval for the mean amount spent per owner for an obedience class.

A) (\$106.29, \$112.37) ; we are $95 \%$ confident that the mean amount spent per dog owner for a single obedience class is between $\$ 106.29$ and $\$ 112.37$ .
B) (\$106.78, $\$ 111.88 )$ ; we are $95 \%$ confident that the mean amount spent per dog owner for a single obedience class is between $\$ 106.78$ and $\$ 111.88$ .
C) (\$106.23, \$112.43) ; we are $95 \%$ confident that the mean amount spent per dog owner for a single obedience class is between $\$ 106.23$ and $\$ 112.43$ .
D) (\$106.74, \$111.92) ; we are $95 \%$ confident that the mean amount spent per dog owner for a single obedience class is between $\$ 106.74$ and $\$ 111.92$ .

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Question 43

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Provide an appropriate response. -A pollster wishes to estimate the number of left-handed scientists. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 6% A previous study indicates that the proportion of left-handed scientists is 9%.

Provide an appropriate response. -When 425 junior college students were surveyed, 190 said they have a passport. Construct a $95 \%$ confidence interval for the proportion of junior college students that have a passport.

Provide an appropriate response. -The grade point averages for 10 randomly selected junior college students are listed below. Assume the grade point averages are normally distributed. Find a $98 \%$ confidence interval for the true mean. $\begin{array} { l l l l l l l l l l } 2.0 & 3.2 & 1.8 & 2.9 & 0.9 & 4.0 & 3.3 & 2.9 & 3.6 & 0.8 \end{array}$

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error - $\mathrm { E } = 3 , \sigma = 7.75 , ( 1 - \alpha ) = 0.95$

Provide an appropriate response. -The June precipitation (in inches) for 10 randomly selected cities are listed below. Construct a $90 \%$ confidence interval for the population standard deviation, $\sigma$ . Assume the data are normally distributed. $\begin{array} { l l l l l l l l l l } 2.0 & 3.2 & 1.8 & 2.9 & 0.9 & 4.0 & 3.3 & 2.9 & 3.6 & 0.8 \end{array}$

Find Critical Values for the Chi-Square Distribution -Find the critical values, $\chi _ { 1 } ^ { 2 } - \alpha / 2$ and $\chi _ { \alpha / 2 } ^ { 2 }$ , for $95 \%$ confidence and $\mathrm { n } = 12$ .

Provide an appropriate response. -A survey of 250 households showed 41 owned at least one snow blower. Find a point estimate for p, the population proportion of households that own at least one snow blower.

State the Properties of Student s t-Distribution -Every Student s t-distribution with n < N, n the number in the sample and N the number in the population, will be less peaked and have thinner tails.

Provide an appropriate response. -Construct a $95 \%$ confidence interval for the population standard deviation $\sigma$ of a random sample of 15 crates which have a mean weight of $165.2$ pounds and a standard deviation of $12.7$ pounds. Assume the population is normally distributed.

Determine t-values -Find the critical t-value that corresponds to $95 \%$ confidence and $n = 16$ .

Choose the one alternative that best completes the statement or answers the question. -A group of 49 randomly selected parrots has a mean age of $22.4$ years with a population standard deviation of 3.8. Compute the $98 \%$ confidence interval for $\mu$ .

Provide an appropriate response. -A survey of 100 fatal accidents showed that in 32 cases the driver at fault was inadequately insured. Find a point estimate for p, the population proportion of accidents where the driver at fault was inadequately insured

Provide an appropriate response. -A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. How large a sample is needed in order to be $99 \%$ confident that the sample proportion will not differ from the true proportion by more than $4 \%$ ?

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error -The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes. Assume = 14 minutes.

Choose the one alternative that best completes the statement or answers the question. -In a random sample of 60 laptop computers, the mean repair cost was $\$ 150$ with a population standard deviation of $\$ 36$ . Compute the $99 \%$ confidence interval for $\mu$ .

Provide an appropriate response. -Construct a $90 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they played video games was $19.6$ with a standard deviation of $5.8$ hours.

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error -The grade point averages for 10 randomly selected students in an algebra class with 125 students are listed below. What is the effect on the width of the confidence interval if the sample size is increased to 20 ? $\begin{array} { l l l l l l l l l l } 2.0 & 3.2 & 1.8 & 2.9 & 0.9 & 4.0 & 3.3 & 2.9 & 3.6 & 0.8 \end{array}$

Choose the one alternative that best completes the statement or answers the question. -A random sample of 150 towns in a western state had an average annual precipitation of $2.86$ inches and a population standard deviation of $0.78$ inches. Compute the $98 \%$ confidence interval for $\mu$ .