8.13 Confidence intervals: homework

Among various ethnic groups, the standard deviation of heights is known to be approximately 3 inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. 48 male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches.

• a
  • i $\overline{x}=$ $\text{\_\_\_\_\_\_\_\_}$
  • ii $\sigma =$ $\text{\_\_\_\_\_\_\_\_}$
  • iii $s_x=$ $\text{\_\_\_\_\_\_\_\_}$
  • iv $n=$ $\text{\_\_\_\_\_\_\_\_}$
  • v $n-1=$ $\text{\_\_\_\_\_\_\_\_}$
• 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 height of male Swedes.
  • i State the confidence interval.
  • ii Sketch the graph.
  • iii Calculate the margin of error.
• e What will happen to the level of confidence obtained if 1000 male Swedes are surveyed instead of 48? Why?

In six packages of “The Flintstones® Real Fruit Snacks” there were 5 Bam-Bam snack pieces. The total number of snack pieces in the six bags was 68. We wish to calculate a 96% confidence interval for the population proportion of Bam-Bam snack pieces.

• a Define the Random Variables $X$ and $\hat{p}$ , in words.
• b Which distribution should you use for this problem? Explain your choice
• c Calculate $\hat{p}$ .
• d Construct a 96% confidence interval for the population proportion of Bam-Bam snack pieces per bag.
  • i State the confidence interval.
  • ii Sketch the graph.
  • iii Calculate the margin of error.
• e Do you think that six packages of fruit snacks yield enough data to give accurate results? Why or why not?

A random survey of enrollment at 35 community colleges across the United States yielded the following figures (source: Microsoft Bookshelf ): 6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622. Assume the underlying population is normal.

• a
  • i $\overline{x}=$
  • 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 enrollment at community colleges in the United States.
  • i State the confidence interval.
  • ii Sketch the graph.
  • iii Calculate the margin of error.
• e What will happen to the margin of error and confidence interval if 500 community colleges were surveyed? Why?

From a stack of IEEE Spectrum magazines, announcements for 84 upcoming engineering conferences were randomly picked. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal.

• a Define the Random Variables $X$ and $\overline{X}$ , in words.
• b Which distribution should you use for this problem? Explain your choice.
• c Construct a 95% confidence interval for the population mean length of engineering conferences.
  • i State the confidence interval.
  • ii Sketch the graph.
  • iii Calculate the m46730.