You operate a restaurant You read that a sample survey by th

You operate a restaurant. You read that a sample survey by the National Restaurant Association shows that 40% of adults are committed to eating nutritious food when eating away from home. To help plan your menu, you decide to conduct a sample survey in your own area. You use random digit dialing to contact an SRS of 200 households by telephone. The SRS finds that 100 of the 200 respondents are concerned about nutrition. We wonder if this is reason to conclude that the percent in your area is higher than the national 40%.

Fill in the blank. (Give your answer to four decimal places.)

What is the probability that X is 100 or larger if p = 0.4 is true?

Solution

H0: Proportion =0.40

Ha: p>0.40

one sided test

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n = 200

z statistic = 0.224

p value = 0.0125

AT 5% significant level we reject null hypothesis, and accept that

actual proportion is greater than 40%

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x follows a normal distribution with p = 0.40 and variance = 0.4(0.6).200 = 0.0346

P(X>100) = P(Z>0.5-0.1/0.0346) = P(z>4.26) = 0.000