Question

we are interested in looking at ticket prices of MLB games. It is known from past information that the average prices are $26.30 with the population standard deviation of $2.30. Suppose we take a sample of the last five years and find that the average ticket price is $29.94. We are interesting in seeing f the average price of tickets has significantly increased. Use alpha = 0.10. Find the 90% confidence interval for the ticket price.

Answer 1

Here claim is that the average price of tickets has significantly increased.

So hypothesis is vs

As population standard deviation is known, we can use z distribution to find test distribution

Using alternative hypothesis we get P value as

As P value is less than alpha we reject the null hypothesis

Hence we have sufficient evidence to support the claim that average price of tickets has significantly increased

Now to find 90% CI, z value is 1.645 as

So Margin of Error is

Hence CI is