Question

8. It was believed that about 1% of all adults are pathological gamblers. Recently the National Gambling Impact Study Commission randomly selected 2417 adults and found that 35 of them were pathological gamblers. Is there evidence to support the claim that more then 1% of adults are pathological gamblers? Use a = 0.05 level of significance. Use three decimal digits after the dot when calculating the sample proportion. Fill in all the information below: H: H: H, rejected? (Answer yes or no) H, accepted? (Answer yes or no) Final conclusion: Is there significant evidence to believe that more then 1% of adults are pathological gamblers? Answer YES or NO):

Answer 1

Here we have: n=2417 x=35 Sample proportion: 35 -- Ô = = 0.014 n 2417 a = 0.05 Hypothesis: H; P = 0.01 H;P>0.01 Test statistics: Z-test z= = = P-p p(1-p) = 1.98 0.014-0.01 0.01(1-0.01) 2417 n

Critical value: Zcrit= za = 20.05 = 1.645 P-value =p (Z >|1.981) = 0.0239 Reject the null hypothesis. Conclusion: Here we have sufficient evidence to reject the null hypothesis. z-observed value is greater than z-critical value. And p-value is less than alpha value

H_o rejected: Yes

H₁ accepted : Yes

Final conclusion: Yes: There is significant evidence to belive that more than 1% of adults are pathological gamblers.