State the null and alternative hypotheses for the test.  (b) Calculate the test statistics.  (c)Determine the rejection region(s) for the test.  (d) State the conclusion for the test giving reasons for your answer.

State the null and alternative hypotheses for the test. (b) Calculate the test statistics. (c)Determine the rejection region(s) for the test. (d) State the conclusion for the test giving reasons for your answer.

The Agriculture Department
of a certain country reported that the average coffee consumption in the
country, in 2014, was 26.0 gallons per person. A recently taken random sample
of 400 residents of the country found a mean coffee consumption of 26.7 gallons
with a sample standard deviation of 6.8 gallons. Assuming that the population
of coffee consumption is normally distributed, test, at the 10% level of
significance, whether the mean coffee consumption is different from the
reported 26.0 gallons, by answering the following:

(a)State the
null and alternative hypotheses for the test.

(b) Calculate
the test statistics.

(c)Determine
the rejection region(s) for the test.

(d) State the
conclusion for the test giving reasons for your answer.

Question 2[10 marks]

Six months after graduating from college,
randomly selected graduates were surveyed to determine their level of job
pressure. The data was inputted into MINITAB Version 17.0 for analysis to
determine whether level of job pressure is independent of gender. The following
output, Exhibit 1, was generated using MINTAB:

Chi-Square
Test for Association: Age (years), Degree of Job Pressure

Rows: Age
(Years)

Columns: Degree of Job Pressure


Low

Medium

High

All

Less than 20

22

18

24

64


20.84

21.58

*



0.06424

0.59346

0.27173


20 – 39

52

48

46

146


47.55

49.23

49.23



0.41687

0.03054

**


40 – 59

60

65

61

186


60.57

62.71

62.71



0.00545

0.08343

0.04677


60 and Above

36

45

45

126


41.03

42.48

42.48


0.61768

0.14915

0.14915


All

170

176

176

522

Cell Contents:

Count





Expected count




Contribution to Chi-square


Chi-Square = 2.640, DF = ***, P-Value
= 0.852

(a)State the
null and alternative hypotheses for the test.

(b) Determine
the missing values “*”, “**” and “***”.

(c)State the
conclusion for the test giving reasons for your answer.

Total marks 20[Graded
out of 4]



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