Answered: A sample of 30 observations is selected…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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Question

A sample of 30 observations is selected from a normal population. The sample mean is 59, and the population standard deviation is 8. Conduct the following test of hypothesis using the 0.02 significance level.

H₀: μ = 62
H₁: μ ≠ 62

a. Is this a one- or two-tailed test? (One-tailed or Two-tailed)

b. What is the decision rule? (Reject H₀ if −2.326 < z < 2.326 or Reject H₀ if z < −2.326 or z > 2.326)

c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

The value of the test statistic is

d. What is your decision regarding H₀? (Reject H_{0 or Fail to reject H0)}

e-1. What is the p-value? (Round your z value to 2 decimal places and final answer to 4 decimal places.)

The p-value is

e-2. Interpret the p-value? (Round your z value to 2 decimal places and final answer to 2 decimal places.)

There is a % chance of finding a z value this large by "sampling error" When H₀ is true.

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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