Question 1 - Sampling Distribution for mean
The length of human pregnancy from conception to birth can be modeled as a distribution that is approximately normal with mean 266 days and standard deviation 16 days. Please answer the following questions.
a) Draw a graph of the distribution. Be sure to draw the distribution with proper shape, label your axis, and show variable values at ± 1, ± 2, and ± 3 standard deviations from the mean. (2 points)
b) According to this model, what percentage of human pregnancies last longer than 279 days? Please interpret your answer. Show the answer graphically on the distribution function you drew in part (a). (3 points)
c) Approximately 7 % of infants are premature. Using this model, find the pregnancy time that would result in a premature birth. Please interpret your answer. (3 points)
d) A random sample of 4 individuals is selected from the population of pregnant woman. Let X be the average pregnancy length of these 4 individuals. Describe the distribution of X and its parameters. (4 points)
e) What is the probability that the four individuals in part (d) will have an average pregnancy length longer than 279 days? (4 points)
Question 2 - Sampling Distribution for proportion
I flip a fair coin ten times and record the proportion of heads I obtain. I then repeat this process of flipping the coin ten times and recording the proportion of heads obtained for many, many times. When done, I make a histogram of my results.
a) About where will the center of my histogram be? Use appropriate notation to describe this fact.
(2 points)
b) What is the standard deviation of the sampling distribution of the proportion pˆ of heads obtained? (3 points)
c) Describe the shape of the sampling distribution of pˆ . Justify your answer. (3 points)
Question 3 - Sampling Distribution for proportion
A College Alcohol Study finds that 67% of college students support efforts to "crack down on underage drinking." The study took a sample of almost 15,000 students, so the population proportion who support the crackdown is very close to p = 0.67. The administration of a large college recently conducted a SRS (simple random sampling) of 100 students and found that 62 of them support the crackdown on underage drinking.
(a) What is the sample proportion who support a crackdown on underage drinking? (2 points)
(b) If in fact the proportion of all students on the campus who support a crackdown is exactly 67%, what is the probability that the proportion in an SRS of 100 students is less than or equal to the proportion found in the administration's sample? Be sure to check all necessary conditions required for your calculation. (5 points)
Question 4 - Sampling methods
Deanna has been hired to visit the local shopping mall to conduct a survey about the upcoming political election. She needs to select respondents at the mall and ask them questions about their voting tendencies. Deanna decides to position herself by the only entrance to the mall and select every 10th shopper entering the mall to participate. Which of the following sampling techniques best describes Deanna's method?
(2 points)
A) cluster
B) probability
C) simple random
D) systematic
Susan would like to conduct a survey of homeowners in the Meadowbrook neighborhood to get their opinions on proposed road modifications in the area. Which of the following is an example of a cluster sample? (2 points)
A) Susan randomly chooses two streets in the neighborhood and selects every home on these streets.
B) Susan selects the first 20 homes that she passes as she walks into the entrance of the neighborhood.
C) Susan selects every third house on each street in the neighborhood.
D) None of these choices describes a cluster sample.
Susan would like to conduct a survey of homeowners in the Meadowbrook neighborhood to get their opinions on proposed road modifications in the area. Which of the following is an example of a stratified sample? (2 points)
A) Susan randomly chooses two streets in the neighborhood and selects every home on these streets.
B) Susan selects the first 20 homes that she passes as she walks into the entrance of the neighborhood.
C) Susan selects every third house on each street in the neighborhood.
D) Susan ensures that her sample contains a number of two-story, split-level, and ranch homes in her sample that corresponds to the number of homes in the neighborhood.