Question

A manufacturing company finds out that a new process that can decrease their production time. The company only has a limited fund for a process. A standard is set which at least 8% is acceptable for the processing time. 6 trials were undertaken showing a mean production time decrease of 8.4% with a standard deviation of 0.32%. Using a level of significance of (a) 0.01 and (b) 0.05, test the hypothesis that the process should be introduced. Use t-distribution.

Answer 1

Let's take the mean decrease in time = u

Then, null hypothesis (Ho) would be - % (means process should be introduced)

and alternative hypothesis (Ha) would be - % (means process should not be introduced)

We need to find out the p value for which t score is required. ( as t - distribution is to be used )

T score is calculated as- t = (Sample mean - Standard mean)/standard deviation = (8.4 - 8)/0.32 = 0.4/0.32 = 1.25

Degrees of freedom = number of samples - 1 = 6-1 = 5

and it's a one tailed distribution

Put the above values in p value calculator to obtain the p value.

We will get p value = 0.133 (approx)

For both significance levels , 0.01 and 0.05 , p value is greater.

i.e 0.133 > 0.05 and also 0.133 > 0.01

which means in both cases we fail to reject Ho. In other words, there is insufficient evidence that mean decrease in time is less than 8%.