Question

This is a hypothesis test problem................

The Smoky Bear Trucking Company claims that the average weight of a fully loaded moving van is 12,000 lbs. The highway patrol decides to check this claim. A random sample of 30 Smoky Bear moving vans shows that the average weight is 12,100 lbs, with a standard deviation of 800 lbs. Construct a hypothesis test to determine whether the average weight of a Smoky Bear moving van is more than 12, 000 lbs. Use a 5% level of significance.

Find/state the following

a) State the null and alternate hypothesis.
b) Identify the sample as large (normal) or small (student-t) and find critical value
c) Compute z or t value of the sample test statistic
d) Decide whether to reject or not reject null hypothesis

Answer 1

Solution :

Given that ,

= 12000  

= 12100

s = 800

n = 30

Use t - test ,

The null and alternative hypothesis is ,

H0 :   = 12000

Ha : > 12000

This is the right tailed test .

= 0.05  

df = n - 1 = 30 - 1 = 29

t,df = t0.05,29 = 1.699

The  critical value t = 1.699

Test statistic = T

= ( - ) / s / n

= ( 12100 - 12000 ) / 800 / 30

= 0.68

The test statistic = 0.68

df = n - 1 = 30 - 1 = 29

P-value = 0.2509

= 0.05

0.2509 > 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to the test claim .