Answer:
Alternative hypothesis is that Worker productivity is higher with automatic dispensers.
The Rank for Group1 is 115.5 and Group 2 is 55.5.
Conclusion is that Worker productivity is higher with automatic dispensers.
Step-by-step explanation:
The null and alternative hypotheses are
H0: Group1 ≤ Group2 against the claim
Ha: Group1 > Group2
Alternative hypothesis is that Worker productivity is higher with automatic dispensers.
Calculations:
Group1 Group2
Sample Mean x ` 139.22 114.67
Sample size n 9 9
Sample SD 18.21 11.937
Rank 115.5 55.5
U 10.5 70.5
<u><em>The Rank for Group1 is 115.5 and Group 2 is 55.5.</em></u>
<u><em></em></u>
<em><u>1. H0 hypothesis</u></em>
As p-value < alpha and Z lies in the critical region, H0 is rejected.
The randomly selected value of Group1's population is considered have greater productivity than the randomly selected value of Group2's population.
<em><u>2. P-value</u></em>
The p-value equals 0.0046.
<em><u>3. Test statistics</u></em>
<em><u>Z= u-μ+c/σ</u></em>
The critical region for one tailed test for z at 0.01 significance level is
z > 2.33.
The test statistic Z equals 2.6063, which lies in the critical region of acceptance z> 2.326
<u><em>4. Conclusion</em></u>
As the calculated test statistic lies in the critical region H0 is rejected and it is concluded that
<em><u>Worker productivity is higher with automatic dispensers. </u></em>
