Q 20. Let u be the mean serum cholesterol level of the population of 20- to 74-year-old males in a particular countryμand we wish to test the null hypothesis Hoμ ≥ 220mg/100ml at the significance level a = 0.05. We knowthat the standard deviation of the population is o = 60mg/100ml, and the true population mean is as smallas 200mg/100ml.(a) Find the minimum sample size we need so that the power of the test can be at least 95%.(b) If the true population mean is 180mg/100ml instead of 200mg/100ml, describe how the significancelevel and power will be affected, i.e., increased, decreased or unchanged. Justify your answer.(c) If we decrease the significance level, will the power of test be increased? Justify your answer.

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Answered: Q 20. Let u be the mean serum…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Diet Regular μ μ1 μ2 n 20 20 x 0.78646 lb 0.80233 lb s 0.00449 lb 0.00755 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. H0: μ1=μ2 H1: μ1≠μ2 B. H0: μ1=μ2 H1: μ1>μ2 C. H0: μ1≠μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1<μ2 The test statistic, t, is nothing. (Round to two decimal places as needed.) The P-value is…
2. Suppose the chamber of commerce at Pyramid Lake advertises that the average length of trout caught at the lake is μ = 19 inches. However, a fishing magazine survey reported that for a random sample of 51 fish caught, the mean length was x = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of the trout caught at Pyramid Lake is less than μ = 10 inches? (Use α = 0.05)
The mean exam score for 44. male high school students are 19.9 and the population standard deviation is 5.2. The mean exam score for 55female high school students is 19.4 and the population standard deviation is 4.9. At α=0.01, can you reject the claim that male and female high school students have equal exam scores? Complete parts (a) through (e). (a) Identify the claim and state H0 and Ha. What is the claim? A. Male high school students have lower exam scores than female students. B. Male and female high school students have different exam scores. C. Male and female high school students have equal exam scores. D. Male high school students have greater exam scores than female students. What are H0 and Ha? Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.
34) If a population exhibits a skew of -5.00 and an excess kurtosis of 5.00 which of the following is true? The population mean exceeds the median. The population variance exceeds the standard deviation. The population standard deviation exceeds the variance. The population median equals the mean. The population median exceeds the mean.
2. Suppose that we are testing Ho following observed values of the test (a) Zo= 2.45 (b) Zo= -1.53 = po versus H₁>po. Calculate the p-value for the statistic: (c) Zo= 2.15 (e) Zo= -0.35 (d) Zo = 1.95
Total fat content (including saturated fat and trans fats) is a key characteristic of cheese. Assume that for a given type of cheese, total fat content (10-1 g/g of cheese) follows a normal distribution with a population mean of 2.85 (unit) and a population variance of 0.01 (unit2). Such an assumption is reasonable because fat content varies inside cheese and the “errors” around the mean total fat content (i.e. the value appearing on the etiquette) are distributed like a bell shape. a) What is the probability that the total fat content of this cheese exceeds 3 (unit)? b) What is the probability that the total fat content varies from 2.8 to 3 (unit)?
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13. Test a claim that the mean amount of carbon monoxide in the air in U.S. cities is less than 2.31 parts per million. It was found that the mean amount of carbon monoxide in the air for the random sample of 65 cities is 2.37 parts per million and the standard deviation is 2.12 parts per million. At α=0.10, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. Question content area bottom Part 1 (a) Identify the claim and state H0 and Ha. Which of the following correctly states H0 and Ha? H0: muμ greater than or equals≥ 2.31 2.31 Ha: muμ less than< 2.31 2.31 (Type integers or decimals. Do not round.) The claim is the alternative hypothesis. Part 2 (b) Use technology to find the critical value(s) and identify the rejection region(s). The critical value(s) is/are t0=negative 1.30 −1.30. (Use a comma to separate answers as…
Question 7 > You wish to test the following claim (Ha) at a significance level of a = 0.05. H.: 41 Ha: µ1 7 42 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you have reason to believe that the variances of the two populations are equal. You obtain a sample of size nį = 14 with a mean of M1 first population. You obtain a sample of size n2 of SD2 = 7.4 from the second population. = 67.8 and a standard deviation of SD1 19 with a mean of M2 15.5 from the 61.7 and a standard deviation In the answer box below insert 2.0395 as the critical value for this test. (Report answer accurate to three decimal places.) critical value What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = %3D The test statistic is... O in the critical region O not in the critical region
Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Diet Regular μ μ1 μ2 n 26 26 x 0.78073 lb 0.80038 lb s 0.00447 lb 0.00745 lb Question content area bottom Part 1 a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. H0: μ1=μ2 H1: μ1>μ2 B. H0: μ1=μ2 H1: μ1<μ2 Your answer is correct. C. H0: μ1≠μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1≠μ2 Part 2 The test statistic, t, is…
A sample of five cans of standard grade tomatoes in puree was taken at random from a production line immediately after filling, and the solid content of each can was weighed. The company desires to test whether the average weight per can is at the specified level of 22 ounces. Past experience indicates that the distribution of the weights per can is approximately normal. The α risk for the test is to be controlled at .01. For the sample, the mean weight was ?̅ =23.9 and the sample standard deviation was s = 0.822 a. State the null and alternative hypotheses. b. Determine the rejection region – indicate how you did this; don’t just give the answer. c. Compute the test statistic – indicate what formula was used. d. What is your conclusion and why?

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