Question

A manufacturer claims that the life span of its tires is 50,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 49 comma 785 49,785 miles. Assume sigma σ equals = 800 (ROUND TO FOUR DECIMALS)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 50000

H_a :    50000

Test statistic = z

= ( - ) / / n

= (49785 - 50000) / 800 / 100

= -2.6875

P(z < -2.6875) = 0.0036

P-value = 2 * 0.0036 =  0.0072

= 0.05

P-value <

Reject the null hypothesis .