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. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster? a) Is this a one or two tailed test? Why? b) State the null and the alternative hypothesis. c) What is the decision rule? d) What is the value of the test statistic? (show your work) e) Is the null hypothesis accepted or rejected? ( 1 mark)

Answer 1

Solution :

Given that,

a)

This a right (One) tailed test.

b)

The null and alternative hypothesis is,  

Ho: 42.3

Ha: 42.3

c)

Critical value of  the significance level is α = 0.10, and the critical value for a right-tailed test is

= 1.319

Reject H0. if t > 1.319

d)

The test statistics,

t =( - )/ (s /n)

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

= -3.085

e)

Since it is observed that t = -3.085 < = 1.319, it is then concluded that fail to reject the null hypothesis.