Question

A marketing professor asked a random sample of college students who have cell phones how much their monthly bill was. He found the sample mean was $100. Using a two-tailed significance test, he rejected Ho: µ = $80 using the usual decision cutoff of α = 0.05. Which one of the following could be a 95% confidence interval for the mean monthly cell phone bill for all college students with cell phones?

Show your reasoning.

a) ($70, $110)

b) ($70, $130)

c) ($80, $130)

d) ($90, $110)

e) ($100, $140)

Answer 1

He found the sample mean was $100.

he rejected Ho: µ = $80 using the usual decision cutoff of α = 0.05.

u = 80

So here we reject Ho.it means that the value of u is other than 80.

So we reject Ho using confidence interval if confidence interval does not include the u value.

Here we reject Ho using confidence interval if confidence interval does not include the 80 value.

from answers the confidence interval does not include 80 is (90,110) & (100,140)

Now we know that,

xbar = 100

The 95 % confidence interval for u is ( 100 +- margin of error)

So final confidence interval will be around 100. & 100 should be included in it.

So 100 cannot be lower bound of an confidence interval.

So final answer will be (90,110)

Answer:- ($90,$110)