Question

Q 1 A survey of 200 workers was conducted regarding their education (school graduates or less, college graduates, university graduates) and the level of their job satisfaction (low, medium, high). These are the results:

	Low	Medium	High
School	20	35	25
College	17	33	20
University	11	18	21

We will test at a 0.025 level of significance whether the level of job satisfaction depends on the level of education. (Critical Value = 11.14)                                       

Q 2 Four hostels took a random sample of students regarding their grade averages for the past term. The results are shown below:

Hostel 1	Hostel 2	Hostel 3	Hostel 4
2.17	2.63	2.63	3.79
1.85	1.77	3.78	3.45
2.83	3.25	4	3.08
1.69	1.86	2.55	2.26
3.33	2.21	2.45	3.18

Use a significance level of 1%, is there a difference in grade averages among the hostels? (Critical Value = 4). Also make the ANOVA summary table.                   

Q 3 Researchers are interested in the mean age of a certain population. A random sample of 32 individuals drawn from the population of interest has a mean of 27. Assuming that the population is approximately normally distributed with variance 20, can we conclude that (a) the mean is different from 30 years (b) the mean is greater than 30 years (c) the mean is less than 30 years ? (α=0.05) .                                                                        

Q 4 A certain company would like to determine the amount of time employees waste at work each day. A random sample of 10 of its employees shows a mean time of 121.80 minutes wasted per day with a standard deviation of 9.45 minutes per day. Does the data provide evidence that the mean amount of time wasted by employees each day is more than 120 minutes? Test at α=.05. Assume the population is at least approximately normally distributed.                                                                                                 

Q 5 The government is concerned that in Pakistan the percentage of deaths of Sindhi prisoners was higher than the per cent of deaths of other prisoners, which is 0.25%. A sample of six years was collected, and 51 out of 14,495 Sindhi prisoners died. Does data provide evidence to show that the proportion of deaths of Sindhi prisoners is more than 0.25%?

Answer 1

Question 1

Here,

H₀ : Type of institution is independent of Level of satisfaction.

H_a : Type of institution is dependent of Level of satisfaction.

Observed Value

	Low	Medium	High	Total
School	20	35	25	80
College	17	33	20	70
University	11	18	21	50
Total	48	86	66	200

Expected value  = Total values in row * Total value in column/Total population

	Low	Medium	High	Total
School	19.2	34.4	26.4	80
College	16.8	30.1	23.1	70
University	12	21.5	16.5	50
Total	48	86	66	200

Chi-square value = =

	Low	Medium	High	Total
School	0.033	0.010	0.074	0.118
College	0.002	0.279	0.416	0.698
University	0.083	0.570	1.227	1.880
Total	0.119	0.860	1.718	2.696

= 2.696

Here critical value = 11.14

so < _critical

so we would reject the null hypothesis and can conclude that Type of institution is independent of Level of satisfaction.