# Chi- square test, test for difference between means

1) A researcher wishes to determine whether there is a relationship between the gender of an individual and the amount of alcohol consumed. A sample of 68 people is selected and the data are obtained.

Alcohol Consumption

Low Moderate High Total

Gender

Male 10 9.13 9 9.93 8 7.94 27

Female 13 13.87 16 15.07 12 12.06 41

Total 23 23 25 25 20 20 68

i) Show how the expected value of 9.13 was obtained.

ii) At the 5% level of significance can the researcher conclude that alcoholconsumption is related to gender?

iii) Is there any need for concern in performing the test in part (ii)? Give reasons

2) Find the 95% confidence interval for the variance and standard deviation of the nicotine content of cigarettes manufactured if a sample of 20 cigarettes has a standard deviation of 1.6 milligrams

3) A management consultant has to compare the incomes of graduates of MBA programs with those of graduates of Bachelor degrees. In a random sample of 20 incomes five years after getting an MBA degree, the consultant found the mean salary and the standard deviation to be $45,300 and $9,600 respectively. A random sample of 25 incomes five years after getting a Bachelor's degree yielded a mean salary of $43,600 with a standard deviation of $12,300.

Can we infer at the 5% significance level, that the mean salaries of MBA is btter than Bachelor degree graduates.

#### Solution Preview

Answer is in the file attached.

1 A researcher wishes to determine whether there is a relationship between the gender of an individual and the amount of alcohol consumed. A sample of 68 people is selected and the data are obtained.

Alcohol Consumption

Low Moderate High Total

Gender

Male 10 9.13 9 9.93 8 7.94 27

Female 13 13.87 16 15.07 12 12.06 41

Total 23 23 25 25 20 20 68

i) Show how the expected value of 9.13 was obtained.

ii) At the 5% level of significance can the researcher conclude that alcoholconsumption is related to gender?

iii) Is there any need for concern in performing the test in part (ii)? Give reasons

Alcohol Consumption

Low Moderate High Total

Gender

Male 10 9.13 9 9.93 8 7.94 27

Female 13 13.87 16 15.07 12 12.06 41

Total 23 23 25 ...

#### Solution Summary

Answers 3 questions:

1) Chi square test of independence,

2) Confidence interval of variance and standard deviation, and

3) Test of hypothesis for difference between means