Question

A cellphone company is curious about what consumers think of their new smart watch. The company sets up a demo in the Mall of America in Bloomington, Minnesota. The demo shows off the features of the new watch and allows volunteers to try it out. One outcome of the study is a 95% confidence interval for the mean of “the highest price you would pay for our new smart watch”

a. Explain why this confidence interval does not give useful information about the population of all customers.

b. Explain what population the obtained sample of customers represents.

c. The company found that the average of the 80 customers sampled was $316 ( for the highest price they would pay for the smart watch. Given the population standard deviation, ?, is known to be $60, calculate and interpret the 95% confidence interval for the true population mean. (Hint: decide whether this would be a z-procedure or a t-procedure)

d. How many customers would the cell company need to sample if the desired a margin of error was $15. Use the same t* or z* as in part c.

Answer 1

a

this confidence interval will not give useful information as the sample size is very small and possibly biased as this only takes in account the people who are in the mall at the given time again people might lie and so with a small sample results might vary

b)

population would be all american people who are likely to buy a smart watch

c)

this is a z procedure as sample size > 30

so ci =

316 - 1.96*SE, 316+1.96*SE

SE = 60/sqrt(80) =6.708204

316-13.14808, 316+13.14808

302.9, 329.1

d)

ME =15

1.96*60/sqrt(n) = 15

n= (1.96*4)^2 ~ 64