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 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 πΜ is the proportion of men and πw is the proportion of women. o d (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 i# Zcalc-1.96 b) Calculate the sample proportions. (Round your answers to 4 decimal places.) 1.96 Men 0.4583 Women 0.7353 (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 is (c-2) What is your conclusion? and the p-value is OThe sample shows a significant difference in proportions. O The sample does not show a significant difference in proportions. (d) is normality of p1 -P2 assured? O No Yes 6 求: F2 吕0 F1 F4 F5

Answer 1

Test and CI for Two Proportions

Sample   X   N Sample p
1       11 24 0.458333
2       25 34 0.735294

Difference = p (1) - p (2)
Estimate for difference: -0.276961
95% CI for difference: (-0.525412, -0.0285093)
Test for difference = 0 (vs ≠ 0): Z = -2.14 P-Value = 0.032

c1)
TS = -2.141
p-value = 0.032

c2)
p-value < 0.05
we reject the null hypothesis

A) sample shows a significant difference in proportion

d)
Yes