The Smoky Bear Trucking Company claims that the average weig

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

Solution

The test hypothesis is
Ho:=12000
Ha:>12000

The test statistic is

Z=(xbar-)/(s/n)

=(12100-12000)/(800/sqrt(30))

= 0.68

Given a=0.05, the critical value is |Z(0.05)|=1.645 (check standard normal table)

Since Z= 0.68 is less than 1.645, we do not reject Ho.