Question

A soft drink manufacturer uses fire agents to handle premium distribution for is various products. The marketing director desired to study the timeliness with which the premiums are distributed. Twenty transactions for each agent were selected at random and the time lapse (in days) for handling each transaction was determined. The results follow: Agent 1 Agent 2 Agent 3 Agent 4 Agent 5 24 18 10 15 33 24 20 11 13 22 29 20 8 18 28 20 24 12 16 35 21 22 12 12 29 25 29 10 19 28 28 23 14 10 30 27 24 9 18 31 23 28 8 11 29 2 21 19 11 17 28 24 24 16 15 33 26 25 12 12 30 23 21 18 13 32 24 20 14 13 33 28 24 13 14 29 23 22 11 17 35 23 19 14 16 32 27 26 9 17 26 26 22 11 14 30 25 21 12 16 29 Test at the 0.05 level if on average all agents the same average time lapse. If the null hypothesis is rejected, state which agent has the different time lapse.

Answer 1

ANOVA Table:

ANOVA-Single Factor unt oups Column an 491 24.55 6.1552631579 22.55 8.8921052632 11.75 6.6184210526 14.8 6.3789473684 9.5684210526 Column 2 Column3 Column4 20 20 20 451 235 296 mn urce of Variat SS Between Grou df 4430.1 714.65 5144.75 critical -value 4 1107.525 147.2257398727 7.97749E-40 2.46749362 95 7.5226315 Within Groups tal

The F statistic value from the data is 147.226 and The F critical value is 2.47

Since F statistic value > F critical value we reject the null hypothesis that all the group means are equal at 5% level of significance. It may be interpreted as at least one group mean is different from others at 5% significance level

Now for the interpretation at
a-0.05
i.e at 5%% significance level we can compare the p value which almost 0 from the table. Since the p value < 0.05($\alpha$) we reject the null hypothesis that all the group means are equal

F-test F-test Agent 1 ent 5 3016.155265 20 en agen 24.55 22.55 15526316 8.89210526 20 19 24.55 an an 9.56842105 6.15526316 20 19 Observations df 20 Observations df 55451047 0.344572 0.69221663 two-tail 0.43007392 two-tail

There are three main assumptions that are followed before performing an F-test.

• Equality of variances of the 5 samples

Sample 1,3,4 have variances almost similar. Only sample 2 and 5 shows slight variations. So to check whether the variances of 2 and 5 are statistically equal I performed an F test for the equality of agents 2 and 1 and then agents 5 and 1

• Samples has to taken from a normal population
• samples should be independent. Since the data belong to 5 different agents samples are independent.