Question

# We are interested in looking at ticket prices of MLB games. It is known from past...

We are interested in looking at ticket prices of MLB games. It is known from past information that the average price is \$26.30, with a population standard deviation of \$2.32. Suppose we take a sample of the last 5 years and find that the average ticket price is \$29.94. We are interested in seeing if the average price of tickets has significantly increased. Use alpha=.10.

Find the 90% confidence interval for ticket price.

the null and alternative hypotheses are

What is the critical value?

What is the test statistic?

sample mean, xbar = 29.94
sample standard deviation, σ = 2.32
sample size, n = 5

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

ME = zc * σ/sqrt(n)
ME = 1.64 * 2.32/sqrt(5)
ME = 1.7

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (29.94 - 1.64 * 2.32/sqrt(5) , 29.94 + 1.64 * 2.32/sqrt(5))

CI = (28.2384 , 31.6416) upto 4 decimal

CI = (28.24 , 31.64) upto 2 decimal

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 26.3
Alternative Hypothesis, Ha: μ > 26.3

Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.282.
Hence reject H0 if z > 1.282

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (29.94 - 26.3)/(2.32/sqrt(5))
z = 3.51