1st Edition

ISBN: 9781938168208

Author: Barbara Illowsky, Susan Dean

Publisher: OpenStax College

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Chapter 10, Problem 13P

Two Population Means with Unknown Standard Deviations

Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for

independent group means, population standard deviations, and/or variances known
independent group means, population standard deviations, and/or variances unknown
matched or paired samples
single mean
two proportions
single proportion

A sample of 12 in-state graduate school programs at school A has a mean tuition of $64,000 with a standard deviation of $8,000. At school B, a sample of 16 in-state graduate programs has a mean of $80,000 with a standard deviation of $6,000.On average, are the mean tuitions different?

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 10, Problem 12P

Chapter 10, Problem 14P

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The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the distance hit by the legendary champion Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. Brand 1: 275, 286, 287, 271, 283, 271, 279, 275, 263, 267 Brand 2: 258, 244, 260, 265, 273, 281, 271, 270, 263, 268 a) Is there evidence to support the claim that the standard deviation of overall distance is the same for both brands of balls (use α = 0.05)? b) Is there evidence to support the claim that the mean of the overall distance is the same for both brands of balls (use α = 0.05)?

Use technology to find (a) the multiple regression equation for the data shown in the accompanying table, (b) the standard error estimate and interpret the result, and (c) the coefficient of determination and interpret the result. The accompanying table shows the total square footages (in billions) of retailing space at shopping centers, the numbers (in thousands) of shopping centers, and the sales (in billions of dollars) for shopping centers for eight years. Click the icon to view the data table on shopping center sales. (a) What is the regression equation? ŷ = 1 + ( )×₁ + (1)×2 (Round to two decimal places as needed.) (b) The standard error is ☐ (Round to two decimal places as needed.) Interpret the standard error. Choose the correct answer below. Shopping center sales Sales, y Total square footage, X₁ Shopping centers, X2 123.4 211.5 385.6 475.5 641.3 716.5 768.2 806.8 851.7 893.9 933.7 1.3 2.8 3.3 3.7 4.1 4.6 4.7 4.8 4.9 5.0 5.1 13.6 17.3 22.2 25.5 32.8 38.0 39.1 39.2 40.5 41.2…

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Chapter 10 Solutions

Introductory Statistics

Ch. 10 - Two samples are shown in Table 10.2. Both have...Ch. 10 - A study is done to determine if Company A retains...Ch. 10 - Weighted alpha is a measure of risk-adjusted...Ch. 10 - The means of the number of revolutions per minute...Ch. 10 - Two types of valves are being tested to determine...Ch. 10 - A concerned group of citizens wanted to know if...Ch. 10 - A study was conducted to investigate how effective...Ch. 10 - A new prep class was designed to improve SAT test...Ch. 10 - Five ball players think they can throw the same...Ch. 10 - Two Population Means with Unknown Standard...

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