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In: Statistics and Probability

1）Per the USA Food and Drug Administration, frozen custard must contain 1.4% egg yolk solids and...

1）Per the USA Food and Drug Administration, frozen custard must contain 1.4% egg yolk solids and at least 10% milkfat. If the percentage of egg yolk solids is less than 1.4%, then it legally must be called ice cream. A food chemist is hired on a potential suspicion that Culver’s frozen custard does not meet the legal definition across all their loca- tions, so he decides to sample the vanilla custard at 50 different locations across Wisconsin. The sample mean percentage of egg yolk solids is 1.2%, with a sample standard deviation of 0.5%.
(a) Finda95%confidenceintervalforthetruemeanpercentageofeggyolksolidsforCulver’s vanilla custard. (You should be using the confidence interval for the mean here, not the proportion.) Use the normal distribution.
(b) Ifweweretosetupahypothesistestforthissituationregardingeggyolksolids,whatwould the null and alternative hypotheses be?
(c) What would be a Type I error in this situation? Put your answer in context.
(d) What would be a Type II error in this situation? Put your answer in context.


2）If the distribution of the weights of all people traveling by air between Dallas and El Paso is normal with μ = 163 pounds, and σ = 18 pounds, then
(a) What’s the distribution of the sample mean of the weight of 36 passengers? Be specific and provide the mean and variance.
(b) What is the probability that the sample mean of the weight of 36 passengers exceeds 170 pounds?

Solutions

Expert Solution

1)

(a)

b)

c)

Type I error shows the probability of rejecting the true null hypothesis.

That is researcher incoorectly conclude that true percentage of egg yolk solids is less than 1.4% while actually it is not.

d)

Type II error shows the probability of fail to reject the true null hypothesis.

That is researcher incoorectly conclude that true percentage of egg yolk solids is not less than 1.4% while actually it is less than 1.4%.

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2(a)

(b)

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orchestra answered 2 years ago
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