Question

A fitness magazine claims that the mean cost of a yoga session is not more than $13. You work for a consumer group and are asked to test this claim. You find that a random sample of 27 yoga sessions has a mean cost of $14.32 and a standard deviation of $2.40. At ?-0.025, do you have enough evidence to reject the magazine's claim? Assume the population is normally distributed. a. Ho HA b. Find the critical value (s) and identify the rejection region(s) c. Find the standardized test statistic t d. Decide to reject or fail to reject the null hypothesis e) Interpret the decision in the context of the original claim.

Answer 1

Test: μ > 13 with t dist" Hypothesis test H0 : μ=13 Ha : μ > 13 (Null Hypothesis, Ho : μ < 13 is also correct) (Alternative Hypothesis, also called H1) This is upper tailed test z= 14.32 s 2.4 n-27 Significance Level, α = 0.025 Degrees of freedom df-n-1 26 tcritical-tadf-t0.025df=26-2.056 (from t-table, one-tailed. d.f.-26 ) Critical Value, te2.056 Rejection criteria: Rejection region is in direction of Alternative hypothesis, since Ha : μ > 13, rejection rule is: Reject Ho if test statistic, to > 2.056 Rejection region has been shaded

0.025 2.056 x-μ 14.32-13 tobserved- bseed 2.4/V27 2.858 Test statistic, to Decision: Since to > te, we (REJECT thel hypothesis. Hence at 2.5% significance level, we have sufficient evidence to conclude that μ 2858 is greater than 13 Thank yous