Question

In 1940, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages? Of the 1100 adults surveyed, 363 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 330 indicated that they were total abstainers. Complete parts (a) and (b) below. (a) Determine the sample proportion for each sample. respectively. The proportions of the adults who took the 1940 survey and the recent survey who were total abstainers are and (Round to three decimal places as needed.) (b) Has the proportion of adults who totally abstain from alcohol changed? Use the = 0.01 level of significance. First verify the model requirements. Select all that apply CANA1 (1-1) 10 and 12P2 (1-2) > 10 OB. The sample size is more than 5% of the population size for each sample. OC. The samples are independent. D. The sample size is less than 5% of the population size for each sample. E. The samples are dependent. CF. The data come from a population that is normally distributed. Identify the null and alternative hypotheses for this test. Let p, represent the population proportion of 1940 adults who were total abstainers and D2 represent the population proportion of recent adults who were total abstainers. Determine the null and alternative hypotheses. HO:21 12 H1: P17 P2 Find the test statistic for this hypothesis test. (Round to two decimal places as needed.) Determine the P-value for this hypothesis test. (Round to three decimal places as needed.) Interpret the P-value. out of 100 repetitions of this experiment. If the population proportions are equal, one would expect a sample difference proportion greater than the absolute value of the one observed in about (Round to the nearest integer as needed.) State the conclusion for this hypothesis test. O A. Do not reject Ho. There is sufficient evidence at the a = 0.01 level of significance to suggest the proportion of adults who totally abstain from alcohol has changed. B. Do not reject Ho. There is not sufficient evidence at the a= 0.01 level of significance to suggest the proportion of adults who totally abstain from alcohol has changed. OC. Reject Ho. There is not sufficient evidence at the a=0.01 level of significance to suggest the proportion of adults who totally abstain from alcohol has changed. OD. Reject Ho. There is sufficient evidence at the a=0.01 level of significance to suggest the proportion of adults who totally abstain from alcohol has changed.

Answer 1

a)

sample #1   ----->   1940
first sample size,     n1=   1100
number of successes, sample 1 =     x1=   363
proportion success of sample 1 , p̂1=   x1/n1=   0.3300
      
sample #2   ----->   recent
second sample size,     n2 =    1100
number of successes, sample 2 =     x2 =    330
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.3000

answer: 0.330 , 0.300 resp.

b) option A), C), D)

difference in sample proportions, p̂1 - p̂2 =     0.3300   -   0.3000   =   0.0300
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.3150          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.01981          
Z-statistic = (p̂1 - p̂2)/SE = (   0.030   /   0.0198   ) =   1.51
p-value =        0.130

interpret - equal , greater than the absolute value of , 13 out of 100

conclusion: option B)