Question

1. You have been hired by a company as a Statistical Consultant, for the purpose of determining whether there is a significant difference in the number of units produced by workers on Mondays and Fridays at their factory. The following table indicate the number of units produced by three groups of eight workers randomly sampled from each of the relevant days.

1. Using manual computation, perform the appropriate hypothesis test at α = 0.05

Mondays	Fridays
43	24
27	16
25	33
45	28
32	26
41	17
38	32
24	23

2. You perform a simple experiment to determine whether the consumption of two units of alcohol has a significant impact upon ability to play computer games. Two samples, each of ten game players, are randomly chosen for the experiment. Subjects in both groups are asked to play a computer game for ten minutes, and the final score of each game player is recorded. The first group play the game being sober, while the second group play the game immediately after consuming two units of alcohol. The results obtained are given in the following table:

                      Score

Group 1 (No Units Of Alcohol)	Group 2 (Two Units Of Alcohol)
23	21
22	16
28	17
25	14
25	20
26	19
23	18
26	16
24	17
25	16

2. Perform an appropriate hypothesis test at the 5% significance level to determine whether consumption of two units of alcohol has a significant impact upon ability to play computer games, as measured by the final scores obtained by game players. Show all calculations, both manual, and using MS Excel.

Answer 1

a)

Xˉ1=34.375 and Xˉ2=24.875
Also, the provided sample standard deviations are:

s1 =8.45 and s2 =6.244
and the sample size is n = 8. For the score differences we have

Dˉ=9.5 and sD =10.433

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD= 0

Ha:μD≠ 0

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=7.

Hence, it is found that the critical value for this two-tailed test is tc =2.365, for α=0.05 and df=7.

The rejection region for this two-tailed test is R={t:∣t∣>2.365}.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=2.575>tc =2.365, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0367, and since p=0.0367<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that mean number of products produced in Monday μ1 is different than Friday μ2, at the 0.05 significance level.

NOTE: As per Q&A answering guidelines I have answered the first question please re post the rest.Thank you