1. The kid's toy Bop It[1] was designed such that the population average number of actions a player successfully performs is 4 and the population standard deviation is 2 actions. For this question, assume a sample size of 25 people randomly draw from the relevant population. Show the percent (or proportion) and relevant z-scores.
   1. What percent of such samples would we expect to have an average number of actions over 5?
   2. What percent of such samples would we expect to have an average number of actions under 4.5?
   3. What percent of such samples would we expect to have an average number of actions over 3.5?
   4. What percent of such samples would we expect to have an average number of actions between 3.6 and 4.2?

For problems 2-5, you are asked to calculate a confidence interval. Your calculation should include all intermediate values. Intermediate values include:

• For confidence intervals based on: z,
• For confidence interval based on: df, t,
• For confidence intervals for proportions:z and s_p

1. In a sample of college students (N=20), the average battery percentage on their cellphones was 51, with a standard deviation of 12.
   1. Calculate a 95% confidence interval for battery percentage. Be sure to show all relevant intermediate values.
   2. Interpret the meaning of this confidence interval.
2. In a sample of 30 call center workers, the average number of calls per hour was 10 (s=2.5).
   1. Calculate a 95% confidence interval for the average calls per hour. Be sure to show all relevant intermediate values.
   2. Interpret the meaning of this confidence interval.
3. A recent Pew poll of American adults found that 71% of Americans wanted the federal government to work on strengthening the economy (N=5,128)[2].
   1. Calculate a 99% confidence interval for this proportion. Be sure to show all relevant intermediate values.
   2. Interpret the meaning of this confidence interval.
4. For Problem Set 4, you worked with data on the number of children in a household. In this sample of 60,460 households, the average number of children was 0.80 (s=1.14).
   1. Calculate a 95% confidence interval for the number of children in the household. Be sure to show all relevant intermediate values.
   2. Interpret the meaning of this confidence interval.