Question

Suppose someone claims they can make it in and out of the grocery store in less than 10 minutes. Let's take a sample of 15 shoppers with a mean of 9.8 minutes and a standard deviation of 0.4 minutes. Can the claim at an alpha of 0.05?

Answer 1

Solution :

Given that,

= 10  

= 9.8

= 0.4

n = 15

The null and alternative hypothesis is ,

H0 :   = 10

Ha : < 10

This is the left tailed test .

Test statistic = z

= ( - ) / / n

= ( 9.8 - 10 ) / 0.4 / 15

= -1.94

Test statistic = -1.94

P (Z < -1.94 ) = 0.0262

P-value = 0.0262

= 0.05  

0.0262 < 0.05

P-value < .

Reject the null hypothesis .

There is sufficient evidence to claim the test at an alpha of 0.05