Question

Questions 1 – 3 are based on the following information.

A tobacco cigarettes manufacturer claims that the mean age of males and females starting to smoke cigarettes do not differ. A researcher would like to investigate the manufacturer’s claim and took random samples of 20 females and 30 males from normal populations and the descriptive statistics for the age of the respondents are tabulated below.   Use ^_.

	Females (F)	Males (M)
Sample size ()	20	30
Sample mean ()	20	18
Population standard deviation ()	2.7	2.3

Let:       population mean of the age of the females
   population mean of the age of the males
   
The hypotheses tested are given as:

Given: Test statistic = 2.72

i. The rejection rule for the critical value approach is:
Reject if [a] or [b]

ii. The p-value is:
[c] – 4 decimal places

Answer 1

The null and alternative hypotheses are,

H0 : μfemales - μmales = 0

H1 : μfemales - μmales ≠ 0

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = 2.72

i) Since, we don't have a given significance level, we used 0.05.

Therefore, critical values at significance level of 0.05 are, Zcrit = 1.96

Rejection rule : Reject H0, of z < -1.96 or z > 1.96

ii) p-value = 2 * P(Z > 2.72)

=> p-value = 2 * [ 1 - P(Z < 2.72) ]

=> p-value = 2 * [ 1 - 0.9967 ]

=> p-value = 2 * 0.0033

=> p-value = 0.0066

Since, p-value is less than 0.05, we reject H0.