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value: 33.33 points The top food snacks consumed by adults aged 18-54 are gum chocolate candy,fresh fruit, potato chips, breath mints/candy, ice cream, nuts, cookies, bars, yogurt, and crackers. Out of a random sample of 24 men, 11 ranked sample of 34 women, 25 ranked fresh fruit in their top five snack choices. Is there a difference in the proportion of men and women who rank fresh fruit in their top five list of snacks? (a-1) Choose the appropriate hypotheses. Assume πM is the troportion of men and women. is the proportion of (a-2) State the decision rule for a-05. (Round your answers to 3 decimal places. A negative value should be indicated by a minus sign.) Reject the null hypotheses if Zcalc (b) Calculate the sample proportions (Round your answers to 4 decimal places.) r Zcalc Sample proportion Men Women (c 1 Calculate the test statistic and find the p value. Do not round intermediate calculations. Round your answers to 3 decimal places. A negative value should be indicated by a minus sign.) The value of the test statistic s and the p-value is 6 MacBook Pro
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Answer #1

a-1

d is the correct option

a-2

for 5 % level of significance

reject null hypothesis if -1.96<zcal>1.96

For sample 1, we have that the sample size is 24, the number of favorable cases is X1 so then the sample proportion is 2 0.4583 For sample 2, we have that the sample size is N2 34, the number of favorable cases is X2 so then the sample proportion is P2- 34-0.7353 The value of the pooled proportion is computed as p-MtNz = 24+24-06207 Also, the given significance level is a 0.05 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: 11, 25, This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted(2) Rejection Region Based on the information provided, the significance level is a 0.05, and the critical value for a two- tailed test ise 1.96. The rejection region for this two-tailed test is R-{z : |z| > 1.96) The z-statistic is computed as follows: Pi P2 0.4583- 0.7353 VP(1 p(/n1 +1/72) 0.6207 (1-0.6207) (1/24 +1/34)Since it is observed that rejected 2.141 1.96, it is then concluded that the null hypothesis is Using the P-value approach: The p-value is p 0.0323, and since p concluded that the null hypothesis is rejected. 0.0323<0.05, it is It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion pi is different than p2, at the 0.05 significance level. Confidence Interval The 95% confidence interval for pı-P2 is:-0.525 < p1-P2 <-0.029 0.525 p P20.029

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