The top food snacks consumed by adults aged 18-54 are gum, chocolate candy, fres

Question

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 fresh fruit in their top five snack choices. Out of a random sample of 37 women, 27 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 pi_M is the proportion of men and pi_ w is the proportion of women. a. H_0: pi_M - pi W = 0 vs, H_1: pi_M - pi_W lessthanorequalto 0 b. H_0: pi_M - pi_W not equal to 0 vs. H_1: pi_ M - pi_ W = 0 c. H_0: pi_ M - pi_ W = 0 vs. H_1: pi _M greaterthanorequalto 0 d. H_0: pi_ M - pi_ W = 0 vs. H_1: pi_ M - pi_W not equal to 0 a b c d (a-2) State the decision rule for a = .10. (Round your answers to 3 decimal places. A negative value should be indicated by a minus sign.) Reject the null hypotheses if (b) Calculate the sample proportions. (Round your answers to 4 decimal places.) (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.) (c-2) What is your conclusion? The sample does not show a significant difference in proportions. The sample shows a significant difference in proportions. (d) Is normality of p_1 - p_2 assured? Yes No

Explanation / Answer

Part-a-1

Option-d is answer as we are testing hypothesis of no difference.

Part-a-2

For =0.10, critical two tailed z=±1.645

Reject the null hypothesis if -1.645<Zcalc>1.645

Part-b

Men Sample proportion pm=11/24= 0.4583

Women Sample proportion pw=27/37 = 0.7297

Part-c-1

Z=(pm-pw)/sqrt(pm*(1-pm)/nm+pw*(1-pw)/nw))

=(0.4583-0.7297)/sqrt(0.4583*(1-0.4583)/24+0.7297*(1-0.7297)/37)

=-2.168

p-value=2*P(Z<-2.168)= 2*0.015=0.030

Part-c-2

The sample show a significant difference in proportions

Part-d

Yes, because in both samples, the success>5.

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