rejection region: null hypothesis

Question

Lodging Cost. A travel association claims that the mean daily lodging cost for two adults traveling together on vacation in San Francisco is at least $240. A random sample of 24 such groups of adults has a mean daily lodging cost of $233 and a standard deviation of $12.50. Is there enough evidence to reject the claim at alpha = 0.10? Notice that the sample size is < 30. Therefore you use the t-test.

Answer 1

H0 or the null hypothesis - the mean daily lodging cost for two adults traveling together on vacation in San Francisco is at least $240

HA or alternate hypothesis - the mean daily lodging cost for two adults traveling together on vacation in San Francisco is < $240

 

Calculate z score = (x - μ)/(s/sqrt(n)) (two-tailed hypothesis)

x = mean of sample = 233

μ = mean of population = 240

s = standard deviation = 12.50

n = population size = 24

z = (233 -240)/(12.5/sqrt(24)) = -2.74

From tables or calculator at alpha = 0.10 and a z score of -2.74, p value < 0.00001 (less than one in a hundred thousand chance of being wrong). The p value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H0) of a study question is true or probability based on chance alone. Since the p value is low we can reject the null hypothesis here.