Question

Question 1​ Production Rates (Please Show all Working Out)

A manufacturing company wishes to find out whether the productivity of its workforce has increased now that they have a new machine. The factory examined the records for a random sample of 8 hours over the past month. The hourly production rates for these 8 hours were:

142 175 162 158 190 154 160 185 173 181

Suppose the production rate before the use of the new machine is 155 units per hour. Test at 5% if the new machine has increased workers’ productivity on average using both the:

(a) ​p-value approach, and

(b)​critical value approach.

Note: For part (a), you should use the “t-dist” function in excel.

Answer 1

First we need to find the mean and SD of the data. Following is the output of descriptive statistics:

Here we have 168, s-15.23, n-10 Hypotheses are Ha: μ >155 Level of significance a-0.05 Test is one tailed (right tailed) Degree of freedom: df -n-1-9 Test Statistics: - (168-155)/(15.23/sqrt(10) -2.699 Critical value: Rejection Region: 1.833 If |t| >1.833, Reject HO Decision: Since test statistics lies in rejection region so we reject the null hypothesis P-value P-value-0.0122 Decision: Since p-value is less than level of significance so we reject the null hypothesis Excel function for critical value: Excel function for p-value: =TINV(0.19 -TDIST(2.699,9,1)

(a)

The p-value is 0.0122

Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that the new machine has increased workers’ productivity.

(b)

The critical value is 1.833

Since test statistics is greater than critical value so reject the null hypothesis That is we can conclude that the new machine has increased workers’ productivity.