Question

The American Automobile Association claims that the meam daily coat for a family of four traveling on vacation in Florida is $118. A random sample of 11 such families has a mean daily meal cost of $128 with a standard deviation of $20. Is there enough evidenfe to reject the claim that alpha = 0.05?

a. Please do a hypothesis test based on t distribution.

b. Please find the rejection region

Answer 1

Given that, sample size (n) = 11

sample mean = $128 and sample standard deviation (s) = $20

a)The null and alternative hypotheses are,

H0 : μ = $118

Ha : μ ≠ $118

Test statistic is,

=> Test statistic is, t = 1.658

b) Degrees of freedom = 11 - 1 = 10

t-critical values at significance level of 0.05 with 10 degrees of freedom are, t^* = ± 2.228

Rejection Region : t < -2.228 or t > 2.228

Since, t = 1.658 < 2.228, we fail to reject the null hypothesis (H0).