Question

The following table summarizes some of the results in the meta-analysis for smokers who used e-cigarettes with nicotine.

	total Sample	Number who stopped smoking
Study 1	464	93
Study 2	289	21
Study 3	200	22
Study 4	35	16
Study 5	40	5
Study 6	214	67

Answer the following questions:

1. Find the total number of smokers in all six studies and the total number who stopped smoking.
2. Find a new confidence interval for the proportion of smokers who stopped smoking using these results.

• The total number of smokers:
• Total number who quit:
• The overall proportion of smokers who quit:
• margin of error
• The confidence interval for proportion who quit: Use 0.05 significance level.

2. Use the combined results to test the claim that fewer than 20% of smokers who use e-cigarettes with
nicotine are able to stop smoking. Use the p-value method

Answer 1

Answer the following questions:

1. Find the total number of smokers in all six studies and the total number who stopped smoking.

Total number of smokers in all six studies = 464 + 289 + 200 + 35 + 40 + 214 = 1242

NUmber who stopped smoking = 93 + 21 + 22 + 16 + 5 + 67 = 224

1. Find a new confidence interval for the proportion of smokers who stopped smoking using these results.

Here we have to find 95% confidence interval for population proportion.

95% confidence interval for p is,

p^ - E < p < p^ + E

p^ = 224 / 1242 = 0.18

E is the margin of error.

For 95% confidence Zc = 1.96

Lower limit = p^ - E = 0.18 - 0.02 = 0.16

Upper limit = p^ + E = 0.18 + 0.02 = 0.20

95% confidence interval for p is (0.16, 0.20)

2. Use the combined results to test the claim that fewer than 20% of smokers who use e-cigarettes with nicotine are able to stop smoking. Use the p-value method

Hypothesis for the test is,

H0 : p = 20% = 0.20 Vs H1 : p < 20%

where p is population proportion.

Assume alpha = level of significance = 0.05

We can do this test in ti-83 calculator.

steps :

STAT --> TESTS --> 5 : 1-PropZTest --> ENTER --> Input all the values --> Alternative : < p0 --> Calculate --> ENTER

Test statistic = -1.73

P-value = 0.0417

P-value < alpha

Reject H0 at 5% level of significance.

COnclusion : There is sufficient evidence to say that the population proportion is less than 20%.