Question

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Let us look back at the same sample selected for you above. In general, lung cancer studies would collect samples that consist of 50% smokers and 50% non-smokers. In fact, I claim that this study contains more than 51% smokers. We will test this claim, using a 1% level of significance. A. State the null and alternate hypothesis: (use </= for Sor >/=for if you need to) H : H: B. State the test statistic for your sample. C. State the p-value for your sample. D. What is your decision based on this p-value? (Reject or fail to reject) the null hypothesis? E. Fill in the blanks to complete the conclusion to this hypothesis test: At the % level of significance, the data (does or does not) show that the of cancer study participants is greater than 51%.

Answer 1

Let P be the proportion of smokers of cancer study participants.

A. We have to test the hypothesis

proportion of smokers of cancer study participants is more than 51%.

i.e. Null Hypothesis - Ho: P= 0.51

against

Alternative hypothesis- Ha : P > 0.51 ( right-tailed test).

B. n = number of participant = 20

number of smokers =10

p =sample proportion of smoker = 10/20 = 0.50

we use one sample z-test for testing population proportion.

Value of test statistic

$z=\frac{p-P}{\sqrt{P*(1-P)}/n}\sim N(0,1)$

$z=\frac{0.50-0.51}{\sqrt{0.51*0.49}/20}=-0.0895$

Value of test statistic t = -0.0895

C. Since test is right-tailed and value of test statistic is -0.0895

p-value is obtained by

D. Alpha: level of significance = 0.05

since p-value > alpha, we failed to reject the null hypothesis.

E.  Conclusion : At 1% level of significance the data does not show that the proportion of smokers of cancer study participants is greater than 51%.