Question

A group of physicians from Denmark conducted a year-long study of the effectiveness of nicotine chewing gum in helping people stop smoking. The 113 people who participated in the study were all smokers. Of these, 60 were given a chewing gum with 2 mg of nicotine, and 53 were given a placebo chewing gum with no nicotine. This was a randomized controlled study. All were told to use the gum and refrain from smoking. Results showed that 23 of the smokers given the nicotine chewing gum had remained nonsmokers for the 1-year period while 12 of the smokers given the placebo had remained nonsmokers during the same period. Do these results support the conclusion that nicotine gum can help stop smoking? Test at α = 0.05.

1-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions

In developing patient appointment schedules, a medical center wants to compare the mean time that staff members spend with patients between two offices--one in Cleveland and one in Cincinnati. A random sample of 30 office visits is taken from each office. Estimate the difference with a 95% level of confidence.

1-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions

Answer 1

Correct option is:

5-Hypothesis test for difference in population means from two independent samples

below are test details:

null Hypothesis:    Ho:    p1-p2		=	0.00
alternate Hypothesis: Ha:   p1-p2		>	0.00
for 0.05 level with right tailed test , critical value of z=			1.645
Decision rule :                   reject Ho if test statistic z > 1.645
	treatment		Placebo
x1                =	23	x2                =	12
p̂1=x1/n1 =	0.3833	p̂2=x2/n2 =	0.2264
n1                       =	60	n2                       =	53
estimated prop. diff =p̂1-p̂2    =		0.1569
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.3097
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0872
test stat z=(p̂1-p̂2)/Se =		1.80

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that nicotine gum can help stop smoking