24. An organization wants to have some merchandise produced that will promote it

Question

24. An organization wants to have some merchandise produced that will promote its cause a an upcoming event. From previous experience, the organization believes that that 35% o event patrons will purchase the merchandise. A promoter for the organization claims that this percentage is not accurate. At a recent event, 60 randomly selected patrons were surveyed, and 18 of those patrons indicated that they would purchase the merchandise. With 90% confidence, is there sufficient evidence to suggest that the percentage of patrons who would purchase the merchandise is different than 35%? Use the step-by-step process for Include the process of determining the test statistic and corresponding p-value as part of your hypothesis test. (If an approximate p-value cannot be determined from the Z cumulative probability table, use bracketing in the t probability table to estimate the p-value range.)

Explanation / Answer

n = 60, p = 0.35, q = 1-p = 0.65, k = 18(occurrence of the desired output)

H0 : p = p0 = 0.35 HA : p 0.35

mean = np = 60*0.35 = 21

variance = npq = 13.65

standard deviation = sqrt(variance) = 3.6946

P(

z = ((K - np) ± 0.5) / npq

z = ((18 - 21) + 0.5) / 13.65

z = -0.676665

p-value for = 0.1

p = 0.249*2, doubling this for a two tailed test, p = 0.498

Fail to reject the null hypothesis

CI is given by

]

CI = (0.3 + 1.645*sqrt(0.3*0.7/60), 0.3 - 1.645*sqrt(0.3*0.7/60)

=(0.397, 0.203)

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