Answered: Per the USA Food and Drug…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 30PPS

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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 locations, 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) Find a 95% confidence interval for the true mean percentage of egg yolk solids for Culver’s vanilla custard. (You should be using the confidence interval for the mean here, not the proportion.) Use the normal distribution.

(b)If we were to setup a hypothesis test for this situation regarding egg yolk solids, what would the null and alternative hypotheses be?

(d) What would be a Type II error in this situation? Put your answer in context.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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