10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

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When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calcul…

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Textbook Question

Chapter 9.2, Problem 42E

In each of Exercises 9.41–9.46, determine the critical value(s) for a one-mean z-test. For each exercise, draw a graph that illustrates your answer.

9.42 A right-tailed test with α = 0.05.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 9.2, Problem 41E

Chapter 9.2, Problem 43E

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(1 point) A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 69 women over the age of 50 used the new cream for 6 months. Of those 69 women, 59 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 60% of women over the age of 50? Test using a =0.01. (a) Test statistic: z = (b) Critical Value: z* = (c) The final conclusion is OA. There is not sufficient evidence to reject the null hypothesis thatp= 0.6. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 60% of women over 50. OB. We can reject the null hypothesis that p 0.6 and accept that p > 0.6. That is, the cream can improve the skin of more than 60% of women over 50.

Chapter 9 Solutions

Introductory Statistics (10th Edition)

Ch. 9.1 - Explain the meaning of the term hypothesis as used...Ch. 9.1 - Regarding the term null hypothesis: a. Originally,...Ch. 9.1 - What role does the decision criterion play in a...Ch. 9.1 - Suppose that you want to perform a hypothesis test...Ch. 9.1 - Suppose that you are considering a hypothesis test...Ch. 9.1 - Suppose that, in a hypothesis test, the null...Ch. 9.1 - Suppose that, in a hypothesis test, the null...Ch. 9.1 - What is the relation between the significance...Ch. 9.1 - Answer true or false and explain your answer: If...Ch. 9.1 - Answer true or false and explain your answer: For...

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In each of Exercises 9.41–9.46 , determine the critical value ( s ) for a one- mean z-test. For each exercise, draw a graph that illustrates your answer. 9.42 A right-tailed test with α = 0.05.

Solution Summary: The author calculates the critical value for the one mean z test, which is 1.645.

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