Question

In a smoking cessation program, over 2000 smokers who were trying to quit were randomly assigned to either a group program or an individual program. With no incentive, the proportion of smokers trying to quit who are still abstaining six months later is about 0.06. Participants in the study were randomly assigned to one of four different incentives, and the proportion successful was measured six months later. Of the 498 participants in the group with the least success, 47 were still abstaining from smoking six months later. We wish to test to see if this provides evidence that even the smallest incentive works better than the proportion of 0.06 with no incentive at all.

  
(a) State the null and alternative hypotheses.

  

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(b) Give the notation for the sample statistic.

  

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(c) Find the value of the sample statistic.

Round your answer to three decimal places.

Value of sample statistic = Enter your answer in accordance to the question statement

the absolute tolerance is +/-0.01

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(d) Use a randomization distribution and the observed sample statistic to find the p-value.

Round your answer to four decimal places.

p-value = Enter your answer in accordance to the question statement

the absolute tolerance is +/-0.01

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(e) Give the mean and standard error of the normal distribution that most closely matches the randomization distribution, and then use this normal distribution with the observed sample statistic to find the p-value.

Round your answer for to two decimal places and your answers for the standard error and the p-value to three decimal places.

Enter your answer in accordance to item (e) of the question statement

Enter your answer in accordance to item (e) of the question statement

p-value = Enter your answer in accordance to item (e) of the question statement

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(f) Use the standard error found from the randomization distribution in part (d) to find the standardized test statistic, and then use that test statistic to find the p-value using a standard normal distribution.

Round your answers to three decimal places.

Enter your answer in accordance to item (d) of the question statement

p-value = Enter your answer in accordance to item (d) of the question statement

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(g) Compare the p-values from the previous parts of the question.

What is the conclusion?

Choose the answer from the menu in accordance to item (g) of the question statement

Do we have evidence that incentives work better than the proportion quitting without any incentive?

Choose the answer from the menu in accordance to item (g) of the question statement

Answer 1