Question

Hi all the answers are given on this worksheet I just need to know how to do part (e) and calculate the two numbers in my TI-84. (I use my TI-84 to get z and p-value)

Problem 4: Two Proportions In 1995, the American Cancer Society randomly sampled 1500 adults of which 555 smoked. In 2005, they surveyed 1730 adults and ound that 578 of them smoked. At the 5% level of significance test the claim that the proportion of smokers in the population decreased over the ten year period. ( pts each) Step 1 Define the parameters, and set up the null and alternative hypotheses. Let pthe proportion of smokers in 1995 and p2 the proportion of smokers in 2005 Then we are interested in testing Step 2 State the test statistic and and its distribution under Ho Because (1) We have two independent random samples. (2) 555 10,1500 55 915 10,58> 10,- 1750-578- 1172 > 10. under Ho, an appropriate test statistic is where p = Step 3 Calculate the observed test statistic and p-value. The observed test statistic is z 2.3685, and p-value is 0.0089. Step 4 Make a decision and state the conclusion. Since p-value = 0.0089 < α = 0.05, we reject Ho. Therefore, we have enough evidence to against that the proportion of smokers in the population did not decrease over the ten year period (e) Form an equivalent confidence interval for the difference between the proportion of smoken in 1995 and 2005. Has the proportion decreased over the ten year period? Note: Please report the Confidence Level) Since this is a one-sided test and 0.05, we should use a 90% confidence level. A 90% CI for pP is (0.0121,0.06733). Because this CI is entirely above 0, so the proportion of smokers in the population has decreased over the ten year period

Answer 1

06 514 2= 0.37-0.33 Sinco- valu 〈 The refore rejecP HD sup port tha O smoker decrasad car pcriocl For cou fidence interval .37)(-63) 1S00 "37-0, 33 ) + (2.58 (0133) (0,67) t CS Scanned with CamScanner

Let the propor Ho Por Ho of smoker q9 s Sompi Tha propostiou of smoker in 20os (Sample smoker u20 apl) ให้ 199s oF p*ople ho smo ke in, 200ST. In 200s TSD 0or Hr Pothesi l ba M.:P, P ht tailed Test Test statistic 1, givcu b = 0.3486 Scanned with CamScanner CS
we have rejected the Null Hypothesis so there is enough evidence to support that proportion of smoker has decreased over the ten year period.