Construct the Indicated Confidence Interval for the Difference Between the Two

question 50

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. Do not assume that the population standard deviations are equal.
-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. $$\begin{array} { r | l } \text { Women } & \text { Men } \\\hline \overline { \mathrm { x } } _ { 1 } = 12.8 \text { hrs } & \overline { \mathrm { x } } _ { 2 } = 14.0 \text { hrs } \\\mathrm { s } _ { 1 } = 3.9 \text { hrs } & \mathrm { s } _ { 2 } = 5.2 \text { hrs } \\\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 17\end{array}$$
Construct a 99% confidence interval for µ1 - µ2, 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) \(- 5.72 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 3.32 \mathrm { hrs }\)
• B) \(- 5.71 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 3.31 \mathrm { hrs }\)
• C) \(- 5.84 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 3.44 \mathrm { hrs }\)
• D) \(- 5.85 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 3.45 \mathrm { hrs }\)

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Definitions:

Interpersonal Disappointments

Feelings of sadness or displeasure caused by the belief that one's personal relationships are not meeting the expected standards or needs.

Grief

A deep emotional response to loss, often involving sadness, longing, and distress.

Sad Mood

A temporary emotional state characterized by feelings of unhappiness and low mood, distinct from clinical depression.

Social Withdrawal

A behavior characterized by a lack of engagement with social or public activities, often due to anxiety, depression, or other psychological conditions.