Question

According to a poll of adults about 42% work during their summer vacation. Suppose that this claim about the population proportion is true. Now if we take a sample of 75 adults, and find the sample proportion p̂ p^ of adults who work during summer vacation.

1. What is the expected value of sample proportion p̂ p^?

2. What is the standard deviation of sample proportion p̂ p^?

3. The shape of the sampling distribution of sample proportion p̂ p^ will be roughly like a
a. uniform distribution
b. student's t distribution
c. normal distribution
d. Poisson distribution
e. binomial distribution

4. P(0.35≤p̂ ≤0.49)=P(0.35≤p^≤0.49)=

5. Is the sample large enough to compute the above probability?
a. Yes, because n≥30n≥30
b. No, the sample size is not sufficiently large. We actually had to assume normally distributed population.
c. Yes, because np≥10np≥10.
d. Yes, because the number of successes and failures are both larger than 10.
e. Yes, because np≥10np≥10 and n(1−p)≥10n(1−p)≥10.

6. Find cc such that P(p̂ ≥c)=0.65

Answer 1