Assignment:
Question 1. The diameter of a brand of ping pong balls is approximately normally distributed, with a mean of 1.30 inches and a standard deviation of 0.04 inches. If you select a random sample of 16 ping-pong balls,
a. What is the sampling distribution of the mean?
b. What is the probability that the sample mean is is less than 1.28 inches?
c. What is the probability that the sample mean is between 1.31 and 1.33 inches?
d. The probability is 60% that the sample mean will be between what two values, symmetrically distributed around the population mean?
Question 2. A random sample of 50 households was selected for a telephone survey. The key question asked was, "do you or any member of your family own a cellular telephone that you can use to access the internet?" Of the 50 respondents, 15 said yes and 35 said no.
a. Determine the sample proportion, P, of households with cellular telephones that can be used to access the internet.
b. If the population proportion is 0.40, determine the standard error of the proportion.
Question 3. A Political Pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least 55% of the vote in the sample, that candidate will be forecast as the winner of the election. If you select a random sample of 100 voters, what is the probability that a candidate will be forecast as the winner when
a. the true percentage of her vote is 50.1%?
b. the true percentage of her vote is 60%?
c. the true percentage of her vote is 49% (and she will actually lose the election)?
d. If the sample size is increased to 400, what are your answers to (a) through ( c)? Discuss
Question 4. In an online survey of 4, 001 respondents, 8% were classified as productivity enhancers who are comfortable with technology and use the internet for it's practical value. Suppose you select a sample of 400 students at your school, and the population proportion of productivity enhancers is 0.08.
a. What is the probability that in the sample, fewer than 10% of the students will be productivity enhancers?
b. What is the probability that in the sample, between 6% and 10% of the students will be productivity enhancers?
c. What is the probability that in the sample, more than 5% of the students will be productivity enhancers?
d. If a sample of 100 is taken, how does this change your answer to (a) through (c)?