Construct the Indicated Confidence Interval for the Difference Between the Two

question 44

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal ( $\left( \sigma _ { 1 } = \sigma _ { 2 } \right)$ , so that the standard error of the difference between means is obtained by pooling the sample variances .
-A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected and each person was asked how many hours he or she had watched television during the previous week.
The summary statistics are as follows.

$\begin{array}{r|r}\text { Women } & \text { Men } \\\hline \overline{\mathrm{x}}_{1}=12.5 \mathrm{hr} & \mathrm{x}_{2}=17.6 \mathrm{hr} \\\mathrm{s}_{1}=4.0 \mathrm{hr} & \mathrm{s}_{2}=4.4 \mathrm{hr} \\\mathrm{n}_{1}=14 & \mathrm{n}_{2}=17\end{array}$
Construct a $95 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

• A) \(- 8.22 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < - 1.98 \mathrm { hrs }\)
• B) \(- 8.48 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < - 1.72 \mathrm { hrs }\)
• C) \(- 7.69 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < - 2.51 \mathrm { hrs }\)
• D) \(- 8.33\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < - 1.87 \mathrm { hrs }\)

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Definitions:

Time And a Half

Refers to the rate of pay that is 50% higher than an employee's regular rate, often used for overtime work.

Gross Earnings

The total income earned by an individual or business before any deductions or taxes.

Commission Rate

The percentage of a sale price paid to the salesperson or agent responsible for the transaction.

Monthly Quota

Monthly Quota is a specified, quantifiable goal that a person or organization is expected to reach within a month, often used in sales and production.