Question

An industrial supplier has shipped a truckload of Teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 12 ounces printed on each cartridge. To check this claim, a sample of n = 15 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: x = 12.13 ounces, s = 0.30 ounce. To determine whether the supplier’s claim is true, consider the test, H0: µ = 12 vsHa: µ > 12, where µ is the true mean weight of the cartridges. Find the rejection region for the test using α = 0.01.

                        A) z > 2.33

                        B) t > 2.624, where t depends on 14 df

                        C) |z| > 2.58               

                        D) t > 2.977, where t depends on 14 df

Answer 1

Solution :

Given that,

= 12

= 12.13

s = 0.30

n = 15

The null and alternative hypothesis is ,

H₀ :   = 12

H_a : > 12

This is right tailed test.

= 0.01

df = n - 1 = 15 - 1 = 14

t_,df = t_0.01,14  = 2.624

The rejection region is t > 2.624

Correct option :- B) t > 2.624, where t depends on 14 df