1. A random sample of 384 people in a mid-sized city (city one) revealed 112 ind
ID: 3152718 • Letter: 1
Question
1. A random sample of 384 people in a mid-sized city (city one) revealed 112 individuals who worked at more than one job. A second random sample of 432 workers from another mid-sized city (city two) found 91 people who work at more than one job. Find a 99% confidence interval for the difference between the proportions of workers in the two cities who work at more than one job.
Select one:
a. (0.003, 0.159)
b. (0.021, 0.141)
c. (-0.159, 0.004)
d. (0.031, 0.131)
e. Sample sizes aren't large enough to justify using z-procedures
2. Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year's class, however, only 21 out of 32 students named math as their favorite class. The teacher decides to conduct a test of the hypothesis H0 : P = .88. What's the correct value of the standard deviation for this test.
Select one:
a. 0.045
b. 0.057
c. 0.064
d. 0.088
e. 0.073
3.Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year's class, however, only 21 out of 32 students named math as their favorite class. The instructor decides to construct a confidence interval for the true population proportion based on the sample value. What's the correct value for the standard error for this case?
Select one:
a. 0.045
b. 0.057
c. 0.064
d. 0.088
e. 0.084
4. Which of the following statements are true?
Select one:
a. When you're doing inference for two proportions, the number of degrees of freedom is one less than the smaller of the two sample sizes.
b. When comparing two population proportions, either sample proportion can be used as the unbiased estimate of the true population proportion.
c. The sampling distribution of the difference between two proportions will always be normal.
d. If sample sizes are large enough, and if the population is large compared to the sample, we can compare two proportions using a normal approximation to the binomial.
e. None of the above are true.
Explanation / Answer
1. A random sample of 384 people in a mid-sized city (city one) revealed 112 individuals who worked at more than one job. A second random sample of 432 workers from another mid-sized city (city two) found 91 people who work at more than one job. Find a 99% confidence interval for the difference between the proportions of workers in the two cities who work at more than one job.
Anaswer:
a. (0.003, 0.159)
2. Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year's class, however, only 21 out of 32 students named math as their favorite class. The teacher decides to conduct a test of the hypothesis H0 : P = .88. What's the correct value of the standard deviation for this test.
Answer:
b. 0.057
Same answer for part 3. b. 0.057
4. Answer : d. If sample sizes are large enough, and if the population is large compared to the sample, we can compare two proportions using a normal approximation to the binomial.
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