Question

The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes assuming that the assembly time is distributed as Normal. Using the 0.10 level of significance, can we conclude that the assembly time using the new method is faster? Use the critical value method to draw your conclusion.                                                                                                                 

Answer 1

H0: ​ = ​42.3

​​​Ha: < 42.3

Test statistics

t = - / (S / sqrt(n) )

= 40.6 - 42.3 / (2.7 / sqrt(24) )

= -3.08

This is test statistics value.

df = n - 1 = 24 - 1 = 23

t critical value at 0.10 with 23 df = -1.319

Since test statistics < -1.319, we have sufficient evidence to reject H0.

We conclude at 0.10 level that we have enough evidence to support the claim.