Question

1.A pharmaceutical company is testing their new nicotine patch. They randomly assign 100 volunteers to use the patch and finding that 37 had quit smoking after 8 weeks. Compute the 96% confidence interval. You DO need to check CLT here.

2.For # 32 .In the United States, the population mean height for 3-year-old boys is 38 inches. Suppose a random sample of 30 non-U.S. 3-year-old boys showed a sample mean of 37.2 inches with a standard deviation of 3 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Determine whether the population mean for non-U.S. boys is significantly different from the U.S. population mean. Use a significance level of 1%. assume that CLT applies.

The pharmaceutical company in #32 repeats their test, this time randomly assigning 125 volunteers to use the patch and finding that 49 had quit smoking after 8 weeks. Compute the 98% confidence interval, and use it to determine if you can support the company’s claim that over half of people on the patch quit smoking after 8 weeks. You do NOT need to check CLT here.

Answer 1

Result:

1.A pharmaceutical company is testing their new nicotine patch. They randomly assign 100 volunteers to use the patch and finding that 37 had quit smoking after 8 weeks. Compute the 96% confidence interval. You DO need to check CLT here.

n=100, p=37/100=0.37

Both np=100*0.37=37 and n(1-p) = 100*0.63=63 are > 10. CLT applies

Confidence Interval Estimate for the Proportion
Data
Sample Size	100
Number of Successes	37
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.37
Z Value	1.9600
Standard Error of the Proportion	0.0483
Interval Half Width	0.0946
Confidence Interval
Interval Lower Limit	0.2754
Interval Upper Limit	0.4646

95% CI = (0.2754, 0.4646)

2.For # 32 .In the United States, the population mean height for 3-year-old boys is 38 inches. Suppose a random sample of 30 non-U.S. 3-year-old boys showed a sample mean of 37.2 inches with a standard deviation of 3 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Determine whether the population mean for non-U.S. boys is significantly different from the U.S. population mean. Use a significance level of 1%. assume that CLT applies.

= -1.4606            

Table value of t with 29 DF at 0.01 level =2.7564

Rejection Region: Reject Ho if t < -2.7564 or t > 2.7564

Calculated t = -1.4606 , not in the rejection region

The null hypothesis is not rejected.

There is not enough evidence to conclude that population mean for non-U.S. boys is significantly different from the U.S. population mean.

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	38
Level of Significance	0.01
Sample Size	30
Sample Mean	37.2
Sample Standard Deviation	3
Intermediate Calculations
Standard Error of the Mean	0.5477
Degrees of Freedom	29
t Test Statistic	-1.4606
Two-Tail Test
Lower Critical Value	-2.7564
Upper Critical Value	2.7564
p-Value	0.1549
Do not reject the null hypothesis

The pharmaceutical company in #32 repeats their test, this time randomly assigning 125 volunteers to use the patch and finding that 49 had quit smoking after 8 weeks. Compute the 98% confidence interval, and use it to determine if you can support the company’s claim that over half of people on the patch quit smoking after 8 weeks. You do NOT need to check CLT here.

Confidence Interval Estimate for the Proportion
Data
Sample Size	125
Number of Successes	49
Confidence Level	98%
Intermediate Calculations
Sample Proportion	0.392
Z Value	2.3263
Standard Error of the Proportion	0.0437
Interval Half Width	0.1016
Confidence Interval
Interval Lower Limit	0.2904
Interval Upper Limit	0.4936

98% CI = (0.2904, 0.4936)