Answered: Express the null hypothesis and the…

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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Express the null hypothesis and the alternative hypotheses in notation form in the following scenario

1. The principal of the school claims that the mean age of the teachers is 45 years. The mean age of the randomly selected 35 teachers is 42 years, which is not equal to what is claimed by the principal.

2. The mathematics teacher claims that the mean IQ of Statistics students is 110. The mean IQ of the 32 randomly selected Statistics students is 112 which is more than what the mathematics teacher claims.

3. It is claimed that the percentage of viewers tuned to Channel 7's new sitcom is 30%. Out of the 250 viewers randomly selected, only 29% are tuned to Channe; 7's new sitcom. Can it be concluded that the percentage of viewers tuned to Channel 7's new sitcom is less than 30%?

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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