# Assignment 3

Question

Assignment 3

Part I: Sampling and Sampling Distributions

1. It has been estimated that 53% of all college students change their major at least once during the course of their college career. Suppose you are told that the sample proportion for a random sample was 0.48. Furthermore, you are told that the probability of getting a sample proportion of this size or smaller is 14%. What must have been the sample size?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

In taking a sample of n observations from a population of N members, the variance of the sampling distribution of the sample means is.jpg”>= .jpg”>.jpg”>. The quantity .jpg”> is called the finite population correction factor.

2) To get some feeling for possible magnitudes of the finite population correction factor, calculate it for samples of n= 15 observations from populations of N = 15, 30, 60, 100, 500, 1,000, 5,000, and 10,000 members.

3) What is the value of the sample variance such that 5% of the sample variances would be less than this value?

4. . Prairie Flower Cereal Inc. is a small but growing producer of hot and ready-to-eat breakfast cereals. The company was started in 1910 by Gordon Thorson a successful grain farmer. You have been asked to test the cereal-packing process of 18 oz (510-gram) boxes of sugar-coated wheat cereal. Two machines are used for the packaging process. Twenty samples of five boxes each are randomly sampled and weighed. The data are contained in the file Sugar Coated Wheat.

a. Compute the overall sample mean, sample variance, and variance of the sample means for each sample.

b. Determine the probability that a single sample ocean is below 500 if the process is operating properly for each machine.

c. Determine the probability that a single sample Clean is above 508 if the process is operating properly for each machine.

5. A consumer product chat has flourished in the last few years is bottled natural spring water. Jon Thorne the CEO of a company that sells natural spring water. He has requested a report of the filling process of the 24 oz (710 mL) bottles to be sure that they are being properly filled. To check if the process needs to be adjusted, Emma Astrom, who monitors the process, randomly samples and weighs five bottles every 15 Minutes for a 5-hour period. The data are contained in the data file Bottles.

a. Compute the sample mean, sample standard deviations for individual bottles, and the standard deviation of the sample mean for each sample.

b. Determine the probability that the sample means are below 685 mL if the population mean is 710.

c. Determine the probability that the sample means are above 720 mL

6. Another product packaged by Prairie Flower Cereal Inc. is an apple cinnamon cereal. To test the packaging process of 40 oz (1,134-gram) boxes of this cereal, 23 samples of six boxes each are randomly sampled and weighed. The lower and upper acceptance limits have been set at 1,120 grams and 1,150 grams respectively. The data are contained in the data File Granola.

a. Compute the overall sample mean, sample variance, and variance of the sample means for each sample.

Part II:Estimation: Single Population

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

Let X1, X2, X3, and X4 be a random sample of observations from a population with mean ? and variance ?2. Consider the following two point estimators of ?:

.jpg”>1 = 0.10 X1 + 0.20 X2 + 0.40 X3 + 0.30 X4, and

.jpg”>2 = 0.25 X1 + 0.25 X2 + 0.30 X3 + 0.20 X4

7) Show that both the estimators are unbiased.

8) Which estimator is more efficient, (.jpg”>1) or (.jpg”>2)? Explain in detail.

9. A random sample of 1% students at a small university were asked a series of questions such as their status as an American or international student, major, gender, age, year in school, and current GPA. Other questions were asked about levels of satisfaction with campus parking, campus housing, and campus dining. Finally, students were asked if they planned to attend graduate school within five years of their college graduation. These data are contained in the data file Finstad and Lie Study,

a. Estimate the population grade point average with 95io confidence level.

b. Estimate the population proportion of students who were very dissatisfied (code 1) or moderately dissatisfied (code 2) with parking facilities on campus. Use a 90%o confidence level.

c. Estimate the population proportion of students who were at least moderately satisfied (codes 4 and 5) with on-campus food service.

10. A group of business students conducted a survey on their university campus to determine student demand for a particular product, a protein supplement for smoothies. As part of their initial steps they randomly sampled 113 students and obtained data that could be helpful in developing their marketing strategy. The responses to this survey are contained in the data file Smoothies.

a. Find a 95% confidence interval estimate for the population proportion of students who would like supplements such as protein, creature, or energy boosters in their smoothies.

b. Estimate the population proportion of students who consider that they are very health conscious with a 98% confidence level.

c, Of the 113 respondents 77 indicated that they drank smoothies in the afternoon. Determine with 90% confidence an estimate of the population proportion thatdrinks smoothies in the afternoon.

11. The manager of Florin’s Flower Mart obtained customer information that is stored in the data file Florin

a. Estimate the mean age of the store’s customers.

b. Estimate the population proportion of customers that are dissatisfied with the store’s delivery system.

c. Estimate the population mean amount charged to

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