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Problem 6 Suppose the Census Bureau found that the average monthly rent for the population of renters
in the Bay Area is $3,000, and the standard deviation is $1,000. A group of researchers surveys
144 people and wants to know how their sample compares to the population. a. What is the probability that a randomly selected renter in the population pays $3,200 or
more? (3 points) b. What is the probability that the researchers find that the mean monthly rent in their sample
of 144 people is $3,200 or more? (3 points) c. Which distributions did you use for parts a. and b. (population, sample, or sampling)? If your
answers were different for parts a. and b., explain why. (3 points) d. Assuming the researchers find the same sample mean and standard deviation as the Census
Bureau, construct the 95% confidence interval for the mean monthly rent in their sample of 144 people. (3 points) Points: 8

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Problem 7 Suppose you’re planning to survey 100 workers about balancing work and non-work obligations
(e.g., family, school). In your study, the proportion of workers with unpredictable schedules
(less than one week notice) was 0.55. The average number of hours worked per week was 33 and the standard deviation was 35. a. Using the sample statistics above, calculate the standard errors for the proportion of workers
with unpredictable schedules and the average number of hours per week. (6 points) b. Now you want to compare your results to those in
prior research. You read 6 prior studies that each
measured the proportion with low schedule notice and
the average number of hours worked per week for 100
workers. The results from those studies are in the table
to the right. What are the estimated standard errors for
the proportion of workers with unpredictable schedules
and the average number of hours per week based on
prior studies? Use four decimal places for these
calculations. (6 points) Study Proportion low Mean schedule notice hou rs/week
A 0.50 29
B 0.40 35
C 0.60 28
D 0.55 30
E 0.50 33
F 0.45 25 c. 00 the sample statistics from your study seem consistent with the results from past studies? How do you know? (4 points)

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Probability Density Problem 5 A striking trend in recent years has been the strong polarization of political opinions between
Republicans and Democrats. Pew Research has studied this trend by measuring opinions about
a wide range of political issues, which they combine into a scale. This scale is an interval-ratio variable measuring a person’s political ideology ranging from -10 (consistently liberal) to +10
(consistently conservative). Assume the distribution of political views was perfectly normal among individuals in each political party. The distributions are visualized in Figure 5.1, and the means and standard
deviations are given in Table 5.1. Figure 5.1 Democrats Republicans Table 5.1: Means and Standard
Deviations of Political Ideology by Party Mean SD.
Republicans 4.75 3.5
Democrats -4.25 3.25 -10-8-6-4-20246810
Political Ideology Scale a. What percentage of Democrats have more conservative views than the average Republican?
(6 points) b. What percentage of Republicans have more liberal views than the average Democrat (6
points) Points:

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