1. In a study on the nutritional qualities of fast foods, the amount of sodium was measured for a randomsample of 40 hamburgers for a certain fast-food restaurant. The mean sodium content was found to be642 milligrams. Suppose it is known that the standard deviation of sodium for all hamburgers madeby the restaurant is o 38 milligrams and that the sodium content is normally distributed.=a) Compute a 90% confidence interval for the true mean sodium content for all hamburgersmade by this restaurant.b) Determine whether the following statements are true or false (a true statement is always true)i) The true mean sodium content u falls inside the confidence interval you calculated in (a)with probability 0.90.ii) A 90% confidence interval for u based on a larger sample will be wider, since it containsmore data.c) Give the frequentists interpretation of the confidence interval you computed in (a). See page125 of the Class Notes.d) Suppose a spokesman for the restaurant claims that the mean sodium content of theirhamburgers is 630 mg, do you have any reason to doubt their claim?

The sample size is .The sample mean is = 642The population standard deviation = 38

Answered: 1. In a study on the nutritional…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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#21)
2. The National Bank is interested in estimating the difference between the mean credit card balances of its two branches. Independent random samples of credit card customers provide the following results: Branch A n, = 32 Branch B n2 = 36 X, = $500 S, = $150 X, = $375 S2 = $130 Construct an interval estimate of the difference between mean balances. Use a confidence coefficient of 0.99.
The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured. The sample mean is x = 66.2 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of o= 4.1 inches. Suppose the heights of a simple random sample of 100 male sophomores were measured rather than 400. Which of the following statements is true? A) The margin of error for the 95% confidence interval would increase. B) The margin of error for the 95% confidence interval would decrease. C) The margin of error for the 95% confidence interval would stay the same because the level of confidence has not changed. D) The standard deviation owould decrease.
Suppose that Jerry (a baker) wants to find a 95% Confidence Interval for the mean baking time for all of his cider donuts. He takes a random sample of 40 cider donuts over the course of several weeks. He found that the average baking time of the sample was 16.4 minutes with a standard deviation of 2.2 minutes. d. Suppose Jose, another donut maker, states that his cider donuts have a mean baking time of 15 minutes. Is there evidence at the 95% confidence level, to support the claim that the true mean baking times for Jerry’s and Jose’s cider donuts are different? Justify. e. Suppose Lee, another donut maker, states that her cider donuts have a mean baking time of 17 minutes. Is there evidence at the 95% confidence level, to support the claim that the true mean baking times for Jerry’s and Lee’s cider donuts are different? Justify.
56.A random sample of 40 companies with assets over $10 million was surveyed and asked to indicate their industry and annual computer technology expense. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results: Based on the comparison between the mean annual computer technology expense for companies in the tax service and food service industries, the 95% confidence interval shows an interval of -5.85 to 14.85 for the difference. This result indicates that _______________. A.There is no significant difference between the two industry technology expenses B.The interval contains a difference of 20.7 C.Companies in the food service industry spend significantly more than companies in the tax service industry D.Companies in the food service industry spend significantly less than companies in the tax service industry
12. A new manufacturing process of component parts is being considered. Samples were taken improves the proportion of defective components. 1425 of 1500 components from the existing process and 1920 of 2000 components from the new process were found to be non-defective. 75 80 P1 = = 0.05, P2 = 0.04 and Pi - P2 = 0.05 - 0.04 = 0.01 1500 2000 a. Find a 99% confidence interval for the true difference in the fraction of defectives between the existing and the new processes? b. Based on your answer in (a), is there any significant difference between the existing and the new processes? Justify?
A wildlife study is designed to find the mean weight of salmon caught by an Alaskan fishing company. Find the minimum sample size needed in order to construct a 95% confidence interval for the mean weight of such salmon, to within 0.30 pounds. Assume that the standard deviation of 3.10.
A sociologist found that in a sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.2. The population standard deviation is 2.1. a.) Find the 99% confidence interval of the mean number of jobs . b.) What is the point estimator
A random sample was selected from a population having a normal distribution. Calculate a 90% confidence interval estimate for for each of the following situations: (a). = 134, n = 10, s = 3.1 (b). = 3,744, n = 120, s = 8.2 (c). = 40.5, n = 9, = 2.9
The following table provides the Noradrenaline concentration (µmol/g of creatinine) obtained by analyzing the urine of healthy volunteers between twenty and thirty years of age. Male 0,48 0,36 0,20 0,55 0,45 0,46 0,47 0,23 Female 0,35 0,37 0,27 0,29 Can noradrenaline concentrations be considered to be significantly different between the sexes (considering the 95% confidence level)? Carry out the appropriate hypothesis test, clearly showing how the calculated, critical values (confidence level and degrees of freedom) were obtained and concluding in full whether the null hypothesis is true or not.
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