Question

In a locality, 100 persons were randomly selected and asked about their educational achievements. The results were as follows:

Sex

Education

Total

Middle

High School

College

Male Female

12

22

13

13

25

15

50

50

Total

34

26

40

100

Can we say that education depends on sex at 5% level of significance?

04 Feb 2023
Answer :
Word Count : 303

Null hypothesis H0: Education is independent of sex.
Under the null hypothesis expected frequencies can be calculated by using
E_{ij} = frac{R_{i} imes C_{j}}{N}
(i =1,2;j 1,2,3)

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Sex

Education

Total

Rahul

19

22

24

27

24

18

20

19

25

 

Ramesh

26

37

40

35

30

40

26

30

35

45

A random sample of nine college students yielded the following data concerning the number of hours per day each student spent in using mobile phone:

5, 2, 7, 5.5, 3.5, 4, 5, 4.5, 4

Estimate the average number of hours per day spent in using mobile phone by the college students.

Complete the following table:

S.

No.

Test for

Name of the Test

Null and Alternative Hypotheses

Test Statistic

Assumptions for Applying the Test

Decision Rule (in short)

1

Population mean when population variation is known

 

 

 

 

 

2

Population mean when population variation is unknown

 

 

 

 

 

3

Population proportion

 

 

 

 

 

4

Difference of two population means

 

 

 

 

 

5

Two population standard deviation

 

 

 

 

 

6

Difference of two population proportion

 

 

 

 

 

7

Independence of two attributes

 

 

 

 

 

State whether the following statements are true or false and also give the reason in support of your answer.
c) In SRSWOR, the possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nn
d) One-way analysis of variance is a generalization of the two sample t-test.
e) If experimental error is reduced considerably and the efficiency of the design is decreased.
f) If strata are heterogeneous then stratified sampling schemes provides estimates with greater precision.
g) If one wants to convert random numbers selected from two digit numbers 00-99 to uniformly distributed U (0, 1) variables then one has to divide them by 99.

A company is trying to improve the work efficiency of its employees. It has organized a special training programme for all employees. In order to assess the effectiveness of the training programme, the company has selected 10 employees randomly and administered a well-structured questionnaire. The scores (out of 100) obtained by the employees are given in the following table:

S. No

Before Training

After Training

1

60

68

2

62

70

3

67

80

4

64

74

5

66

66

6

63

72

7

69

84

8

63

60

9

60

65

10

62

90

In a city, 36 out of a random sample of 500 men were found to drinkers at a certain date. After the heavy increase in tax on intoxicants, another sample of 100 men in the same city included 6 drinkers. Do you feel that the observed proportion of drinkers decreasing significantly at 1%level?

A sample of 100 tyres is taken from a lot. The mean life of the tyres selected is the sample is found to be 40,000 kms with a standard deviation of 3200 kms. Is it reasonable to suppose the mean life of tyres in the lot as 41,000 kms at 5% level of significance? Also establish 95% confidence limits within which the mean life of tyres in the lot is expected to lie.

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