Question

A public health researcher investigating the prevalence of cigarette smoking among senior high school students found that upon surveying a random sample of 150 male students, 37 responded that they regularly smoked cigarettes. A similar survey of 100 female senior students identified that 18 regularly smoked cigarettes. (a) Calculate the sample proportion of senior male students who smoke. (1 mark) (b) Using your value from part a) manually calculate a 95% confidence interval for the proportion of senior male students who smoke cigarettes. (c) Using your confidence interval, say if there is evidence that the prevalence of smoking in senior male students has changed from the accepted historic level of 30%. (d) Calculate the proportion of female senior students who smoke cigarettes (1 mark) (e) Calculate the pooled proportion of senior students who smoke cigarettes and use this to conduct a hypothesis test manually to determine if the current rate of smoking amongst female senior school students is less than that of their male counterparts. Please use a significance level of 5% and identify the six steps in your hypothesis test.

Answer 1

(a)

the sample proportion of senior male students who smoke = p1 = 37/150 = 0.2467

(b)

So,

q1 = 1 - p1 = 0.7533

n1 = 150

SE =

= 0.05

From Table, critical values of Z = 1.96

Confidence Interval:

0.2467 (1.96 X 0.0352)

= 0.2467 0.0690

= (0.1777 , 0.3157)

So,

95% confidence interval for the proportion of senior male students who smoke cigarettes is given by:

0.1777 < P < 0.3157

(c)
Since 0.30 is included in the confidence interval, we conclude that there is no evidence that the prevalence of smoking in senior male students has changed from the accepted historic level of 30%.

(d)

the sample proportion of senior female students who smoke = p2 = 18/100 = 0.18

(e)

the pooled proportion of senior students who smoke cigarettes is given by:

Step 1:
H0: Null Hypothesis: P1P2

Step 2:

HA: Alternative Hypothesis: P1 > P2

Step 3:

= 0.05

Critical value of Z = 1.64

The Rejection Region is:

R = { Z : Z > 1.64}

Step 4:

The Test statistic is given by:

Step 5:

Since calculated value of Z = 1.247 is less than critical value of Z = 1.94, the difference is not significant. Fail to reject null hypothesis.

Step 6:

The data do not support the claim that the current rate of smoking amongst female senior school students is less than that of their male counterparts.