Question

VII. Samples of 10 taken in 1985 and 1995 revealed the average time people Data set for those using statistics spend grocery shopping decreased from 18 minutes to 14 minutes. Respective standard deviations were 5 minutes and 4 minutes. Test at the .10 level of significance whether there has been a change in shopping time variability. software Shopping Time 1985 19 17 18 16 18 1995 10 17 20 16 13 18 15 14 23 28 18 VIII. Test at the .05 level of significance whether workplace accidents happen equally throughout the workweek. Analysis of Workplace Accidents Day Monday Tuesday Wednesday Thursday Friday Totals Accidents 5 10 35

Answer 1

In the first part we calculate the ratio s1 square to s2 square. This is 25/16 = 1.5625

The null hypothesis is Ho sigma 1 square = sigma 2 square

The alternate is they are not equal

The critical value is F with Degree of freedom 9 and 9 and level of significance 5 per cent as the test is two sided.

The critical value of f is 3.137

As the calculated value is less than the critical value we conclude that there is no significant change in variability

In the second question we have to perform a child square test

The expected frequencies for each day is 35/5=7 as we expect the accidents to be uniformly distrubuted

We calculate the test statistic sigma observed - expected square / expected for each cell

Eg for Monday this value is (9-7) square / 7 = 0.57

Similarly the values for the other days are

Tuesday 0.57

Wednesday 0.142

Thursday 0.57

Friday 1.285

We add all of these to get the Calculated value as 3.147

The critical value is childish squats with 5-1 degree of freedom and 5 per cent alpha = 9.487

As calculated is less than tabulated we do not reject Ho and we conclude that there is not enough evidence to reject that accidents are distributed uniformly throughout the week