During the days of coronavirus, people work most of the time from home. Many offices, schools, universities conduct their works, meetings, classes online. As a result of this new normal, it is assumed that on average, utility expenses per family (electricity, water, gas etc.) increases by 40% per month. For the verification of this assumption, four months data of percentage change of utility expenses of 10 families of similar size is given below and answer the following questions, the data is normally distributed:   Percentage change of utility expenses April 33.65 37.09 29.72 33.42 38.14 34.9 37.35 38.66 22.92 34.19 May 37.19 36.61 40.35 28.19 35.19 37.43 38.03 42.99 30.22 38.8 June 37.13 36.2 43.6 35.31 33.66 28.51 37.67 20.68 38.04 38.43 July 38.84 32.17 34.9 30.17 29.63 27.14 32.17 33.46 36.72 39.64   Writ//e the null and alternative hypothesis for this test. Write your final conclusion about the assumption. What will be the 95% confidence interval for the average percentage change of utility expenses on the basis of given data.

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During the days of coronavirus, people work most of the time from home. Many offices, schools, universities conduct their works, meetings, classes online. As a result of this new normal, it is assumed that on average, utility expenses per family (electricity, water, gas etc.) increases by 40% per month. For the verification of this assumption, four months data of percentage change of utility expenses of 10 families of similar size is given below and answer the following questions, the data is normally distributed:

 

Percentage change of utility expenses

April

33.65

37.09

29.72

33.42

38.14

34.9

37.35

38.66

22.92

34.19

May

37.19

36.61

40.35

28.19

35.19

37.43

38.03

42.99

30.22

38.8

June

37.13

36.2

43.6

35.31

33.66

28.51

37.67

20.68

38.04

38.43

July

38.84

32.17

34.9

30.17

29.63

27.14

32.17

33.46

36.72

39.64

 

  1. Writ//e the null and alternative hypothesis for this test.
  2. Write your final conclusion about the assumption.
  3. What will be the 95% confidence interval for the average percentage change of utility expenses on the basis of given data.
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