Question

2. With the imminent new cigarette packaging legislation, there is a lot of interest at the moment in the proportion of Australians who smoke. If we have an estimate of the proportion who smoke now, then we will have a benchmark against which to judge any change that could be attributed to the legislation. Suppose a survey is conducted on the smoking habits of 5,000 randomly chosen Australians aged 15 years or older. It is found that 784 of the participants in the survey currently smoke. Obtain a 95% confidence interval for the proportion of Australians aged over 15 who currently smoke. HINT: Apply and learn the following systematic approach by circling what is appropriate and find missing words. This is statistical inference related to estimation/hypothesis testing about the population mean/proportion because.... I will use the following formulae for calculating 95% confidence interval ....................................., because............... Do I know all components what I need to substitute into this formula? Y/N List all components which are known.............. List all components which are unknown............ How do I find missing components? Find the 95% confidence interval estimate (include units) Interpret (include units)

Answer 1

2)
p^ +- z * sqrt(p^ * (1-p^/n))

X = 784, n = 5000

p^ = X/n = 0.1568, z = 1.96 for 95% CI

Population PROPORTION Confidence Interval
	sample size =	5000
	sample proportion =	0.1568
	confidence level =	95%
	Number of Decimals in Results =	4
	standard error =	0.005142
	Critical z-value =	1.959964
	Confidence Interval =	0.1568	+/-	0.0100786280273571
	=	( 0.146721371972643, 0.166878628027357)
	≈	( 0.1467, 0.1669)
	We are 95% confident the true population proportion is between 0.1467 and 0.1669.

3)

Population PROPORTION Hypothesis Test
	phat = sample proportion =	0.1568
	n = sample size =	5000
	α = alpha =	0.1
Step 1: State Ho and Ha
	Population parameter comparison value?			0.15
	Is this a LEFT, RIGHT or TWO tailed test?			RIGHT-tailed
	Null Hypothesis:	Ho: p ≤ 0.15
	Alternate Hypothesis:	Ha: p > 0.15
Step 2: State Decision Criteria; Find Critical Values
	Reject Ho if z > 1.282
	or Reject Ho if p-value < α = 0.1
Step 3: Calculate Test Statistic
	Test statistic = z =	1.346600658
	p-value =	0.089054441
Step 4: Make Decision
	Reject Ho
	Reject Ho since p-value (0.0891) IS less than α, alpha, = 0.1.
	Also, Reject Ho since the Test statistic (1.3466) meets the rejection criteria in STEP 2.
Step 5: Summarize Decision
	There is sufficient statistical evidence to reject Ho.

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