Question

A recent study claims that people who travel for business spend an average of $78.00 per day on food. You suspect the real average is less than this. You conduct your own study and find that a random sample of 67 people who travel for business spend an average of $75.00 per day on food with standard deviation $12.00. Perform a hypothesis test using ∝ = 0.01 Step #1: State the null and alternative hypothesis. Identify the claim.Step #2: Find the test value.Which test is needed?Find the p-value?Reject or not to reject null hypothesis?

Answer 1

Solution :

Given that,

Population mean = = 78

Sample mean = = 75

Sample standard deviation = s = 12

Sample size = n = 67

Level of significance = = 0.01

Step - 1

The null and alternative hypothesis is,  

Ho: 78

Ha: 78

Step - 2

The test statistics,

t = ( - )/ (s/)

= ( 75 - 78 ) / ( 12 /67 )

= -2.046

Step - 3

This is a left (One) tailed test,

Step - 4

P- Value = 0.0224

Step - 5

The p-value is p = 0.0224 > 0.01, it is concluded that the null hypothesis is fail to rejected.

Not to reject the null hupothesis.