Question

The management of White Industries is considering a new method of assembling its golf cart. The present method requires 62.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 20 carts, using the new method, was 60.6 minutes, and the standard deviation of the sample was 3.1 minutes. Using the 0.02 level of significance, can we conclude that the assembly time using the new method is faster?

a. What is the decision rule? (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.) Reject H0: μ ≥ 62.3 and accept H1: μ < 62.3 when the test statistic is less than:____

b. What is the value of the test statistic? (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)

Answer 1

Step 1 :

Ho:

Ha:

Step 2

Assuming that the data is normally distributed. Since the population standard deviation is not given we will use t statistics.

n= 20

sample mean = 60.6

sample standard deviation = 3.1

Step 3

level of significance = 0.02

The t-critical value for a left-tailed test, for a significance level of α=0.02

tc = −2.205

Since the t stat ( -2.452) is less than t critical we reject the Null hypothesis. [i.e. t stat is in the rejection area]

ANS

a) Reject H0: μ ≥ 62.3 and accept H1: μ < 62.3 when the test statistic is less than : -2.205

b) t statistics = -2.452