Question

A company is considering a new way to assemble its golf carts. 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 a new method of assembling was 40.6 minutes with a standard deviation of 2.7 minutes. Use a .10 level of significance to determine if there is evidence that the new method if faster. What will be the value of your critical value?  

Answer 1

Solution:

Given:

Sample Size = n = 24

Sample mean = minutes

Sample standard deviation = s = 2.7 minutes

Population mean = minutes.

Level of significance = 0.10

We have to test if there is evidence that the new method if faster.

That is time taken by new method is less than  present method.

Thus we use following steps:

Step 1) State H0 and H1:

Vs

Step 2) Test statistic:

Step 3) Find t critical value:

df = n- 1 = 24 - 1 = 23

One tail area = Level of significance = 0.10

t critical value = -1.319

( it is negative , since this is left tailed test)

Step 4) Decision Rule:

Reject null hypothesis H0, if t test statistic value < t critical value = -1.319 , otherwise we fail to reject H0

Since   t test statistic value = < t critical value = -1.319 , we reject null hypothesis H0.

Step 5) Conclusion:

At 0.10 level of significance , we have sufficient evidence to conclude that the new method if faster.