8.13 Confidence intervals: homework  (Page 4/5)

According to a recent survey of 1200 people, 61% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job.

• a Define the Random Variables $X$ and $\hat{p}$ , in words.
• b Which distribution should you use for this problem? Explain your choice.
• c Construct a 90% confidence interval for the population proportion of people who feel the president is doing an acceptable job.
  • i State the confidence interval.
  • ii Sketch the graph.
  • iii Calculate the margin of error.

A survey of the mean amount of cents off that coupons give was done by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

• a
  • i $\overline{x}=\text{\_\_\_\_\_\_\_\_}$
  • ii $s_x=\text{\_\_\_\_\_\_\_\_}$
  • iii $n=\text{\_\_\_\_\_\_\_\_}$
  • iv $n-1=\text{\_\_\_\_\_\_\_\_}$
• b Define the Random Variables $X$ and $\overline{X}$ , in words.
• c Which distribution should you use for this problem? Explain your choice.
• d Construct a 95% confidence interval for the population mean worth of coupons.
  • i State the confidence interval.
  • ii Sketch the graph.
  • iii Calculate the margin of error.
• e If many random samples were taken of size 14, what percent of the confident intervals constructed should contain the population mean worth of coupons? Explain why.

An article regarding interracial dating and marriage recently appeared in the Washington Post . Of the 1709 randomly selected adults, 315 identified themselves as Latinos, 323 identified themselves as blacks, 254 identified themselves as Asians, and 779 identified themselves as whites. In this survey, 86% of blacks said that their families would welcome a white person into their families. Among Asians, 77% would welcome a white person into their families, 71% would welcome a Latino, and 66% would welcome a black person.

• a We are interested in finding the 95% confidence interval for the percent of all black families that would welcome a white person into their families. Define the Random Variables $X$ and $\hat{p}$ , in words.
• b Which distribution should you use for this problem? Explain your choice.
• c Construct a 95% confidence interval
  • i State the confidence interval.
  • ii Sketch the graph.
  • iii Calculate the margin of error.

Refer to the problem above.

• a Construct three 95% confidence intervals.
  • i Percent of all Asians that would welcome a white person into their families.
  • ii Percent of all Asians that would welcome a Latino into their families.
  • iii Percent of all Asians that would welcome a black person into their families.
• b Even though the three point estimates are different, do any of the confidence intervals overlap? Which?
• c For any intervals that do overlap, in words, what does this imply about the significance of the differences in the true proportions?
• d For any intervals that do not overlap, in words, what does this imply about the significance of the differences in the true proportions?