Question

Problem 5: A fitness magazine claims that the mean cost of a meal plan is no more than 12 dollars per day and a standard deviation of 2.60. You researched this topic and found that a random sample of 54 meal plans has a mean cost of 12.85 dollars per day.
a. State the null and alternative hypothesis to test the claim. [5 points]
b. Find the P-value. [5 points]
c. At α = 0.025, do you have enough evidence to reject the magazine claim? State the conclusion. [10 points]

Answer 1

this is the left tailed test .  

The null and alternative hypothesis is ,

H0 :   = 12

Ha : < 12

Test statistic = z

= ( - ) / / n

= (12.85-12) / 2.60/ 54

= 2.40

P(z <2.40 ) = 0.9918

P-value = 0.9918

= 0.025  

P-value >

fail to Reject the null hypothesis .