Past studies have indicated that the percentage of smokers was estimated to be about 32%. Given the new smoking cessation programs that have been implemented, you now believe that the percentage of smokers has reduced. You randomly surveyed 1836 people and found that 552 smoke. Use a 0.05 significance level to test the claim that the percentage of smokers has reduced.a) Identify the null and alternative hypotheses?H0H0: H1H1: b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?left-tailedright-tailedtwo-tailedc) Identify the appropriate significance level.d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.f) Do you reject the null hypothesis?We reject the null hypothesis, since the p-value is less than the significance level.We reject the null hypothesis, since the p-value is not less than the significance level.We fail to reject the null hypothesis, since the p-value is less than the significance level.We fail to reject the null hypothesis, since the p-value is not less than the significance level.g) Select the statement below that best represents the conclusion that can be made.There is sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 32%.There is not sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 32%.The sample data support the claim that the percentage of smokers is less than 32%.There is not sufficient sample evidence to support the claim that the percentage of smokers is less than 32%

Given: Population proportion p=32%=0.32 p= Proportion of smokers Sample size n=1836 Favourable case x=552 # number of smoker Sample proportion p^= x/n= 552/1836 p^=0.3006 Claim: believe that the percentage of smokers has reduced. At 0.05 level of significance Solution: 1): Hypothesis testing: Ho:p=0.32 vs Ha: p<0.32 2):This is left tailed test 3): Appropriate level of significance ɑ =0.05 4): Test statistic Z= (p^-p)/√{p(1-p)/n} Z= (0.3006-0.32)/√{0.32× 0.68/1836} Z=-1.7820 5): Pvalue= P(Z<-1.7820) = NORM. S. DIST(-1.782,TRUE) =0.03737462 Pvalue= 0.0374 (4 d.p)6): Pvalue=0.0374 < 0.05 We reject the null hypothesis, since the p-value is less than the significance level. 7): Conclusion: The sample data support the claim that the percentage of smokers is less than 32% .

Answered: Past studies have indicated that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Past studies have indicated that the percentage of smokers was estimated to be about 32%. Given the new smoking cessation programs that have been implemented, you now believe that the percentage of smokers has reduced. You randomly surveyed 1836 people and found that 552 smoke. Use a 0.05 significance level to test the claim that the percentage of smokers has reduced.

a) Identify the null and alternative hypotheses?

H0H0:

H1H1:

b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?

left-tailed
right-tailed
two-tailed

c) Identify the appropriate significance level.

d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.

e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.

f) Do you reject the null hypothesis?

We reject the null hypothesis, since the p-value is less than the significance level.
We reject the null hypothesis, since the p-value is not less than the significance level.
We fail to reject the null hypothesis, since the p-value is less than the significance level.
We fail to reject the null hypothesis, since the p-value is not less than the significance level.

g) Select the statement below that best represents the conclusion that can be made.

There is sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 32%.
There is not sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 32%.
The sample data support the claim that the percentage of smokers is less than 32%.
There is not sufficient sample evidence to support the claim that the percentage of smokers is less than 32%

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