12.5. A single observation of a random variable having ageometric distribution is used to test the null hypothesis0 = 0o against the alternative hypothesis 0 = 01 > 09. Ifthe null hypothesis is rejected if and only if the observedvalue of the random variable is greater than or equal tothe positive integer k, find expressions for the probabili-ties of type I and type II errors.%3Dvig

Introduction:The probability mass function (pmf) and cumulative distribution function (cdf) of a…

Answered: 12.5. A single observation of a random…

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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Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 15 17 17 20 15 12 13 16 15 12 State the null and alternate hypotheses. H0: ? = 14; H1: ? < 14 H0: ? > 14; H1: ? = 14 H0: ? < 14; H1: ? = 14 H0: ? = 14; H1: ? ≠ 14 H0: ? = 14; H1: ? > 14 What is the value of the sample test statistic? (Round your answer to three decimal places.)
1. A programmer has developed a random number generator that gives a normally distributed set of results based on an input population mean and population standard deviation. To test the program, he inputs a mean of 20 and a standard deviation of 5. He generates 23 random numbers with a sample mean of 21.7 and a sample deviation of 5. He wants to test with 95% confidence whether or not this sample has the correct mean of 20. Which of these is the appropriate null hypothesis? (Ho: µ = 20 or Ho: µ =21.7) What z-value is calculated as the test statistic for this hypothesis? What is the p-value associated with this z? What is the decision? (fail to reject null hypothesis or reject null hypothesis) With 95% confidence based on this measurement, is the program working correctly?
Say that we have a null hypothesis that X1,..., X16 that are Normally distributed with mean 0 and variance 1. Call the sample mean X. Consider the test where p-value = 20 (4 X) - 24 (4|X) – 1 We will reject this if p-value < a. a) Show that the type I error rate of this test is a. b) Say that X1,..., X16 that are Normally distributed with mean 1 and variance 1. What is the type II error rate of this test when a = 0.05? •..
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I need help with this one, please. I need it to be step-by-step please for me to understand.
Test the claim about the differences between two population variances a and o at the given level of significance a using the given sample statistics. Assume that the sample statistics are from independent samples that are randomly selected and each population has a normal distribution. Claim: o so, a = 0.05 Sample statistics: s, = 705, n, =3, s = 368, n, = 9 Find the null and alternative hypotheses. OA Hoio> Hạ: o so3 OC. Hoi o z0 H,: o
8.3
Let X1,..., X be an independent trials process with common expected value 2 and common variance 17. What is the exact value of the expected value of the average A? What is the variance of the average An? Your formula should have n. According to the Chebyshev inequality, P(An 20.2) ≤ (your formula should have n) Using your bound from the Chebyshev inequality, how many trials are needed so that P(An 2≥ 0.2) 0.91? (see the note below here) If you get an answer like n > 123.8, round it up to the next whole number: Your response: 124
Suppose that a random sample X₁, X2, X20 follows an exponential distribution with parameter B. Check whether or not a pivotal quantity exixts, if it exists, find a 100(1 - α)% confidence interval for B. www.
Туре Freq. 11.15 A theory says that in a certain population, half the objects are of type A and the remainder are evenly divided among three types, B, C, and D. A random sample from the population breaks down as shown in the table at right. Does the data show 25 13 8. a statistically significant departure from what the theory predicts? Test using a = .05. ABCD
Suppose it has previously been claimed that the proportion of adults in a certain city that have a university degree is 0.41, and suppose we wish to carry out a test of the null hypothesis that this is the true proportion. In a random sample of 1400 adults in this city, 587 have a university degree. What is the value of the appropriate Z test statistic? (Give your numeric response to at least 3 decimal places. Give only your numeric response, and not any extra characters or symbols. If the value is negative, include the negative sign)
sample of n = 12 young adults who each experienced 5 or more different homes before they were 16 years old questionnaire for which the general population has an average score of µ = 40 in terms of well being scores for this sample : X 38 37 41 35 42 40 33 33 36 38 32 39 , is well-being for frequent movers significantly different from well-being in the general population? Use a two-tailed test with α = .05. State the hypotheses. H0: H1:

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