You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. Ho:μ=77.5Ho:μ=77.5 Ha:μ≠77.5Ha:μ≠77.5You believe the population is normally distributed and you know the standard deviation is σ=18.6σ=18.6. You obtain a sample mean of M=70.5M=70.5 for a sample of size n=16n=16.What is the critical value for this test? (Report answer accurate to three decimal places.)critical value = ±±What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = The test statistic is...in the critical regionnot in the critical regionThis test statistic leads to a decision to...reject the nullaccept the nullfail to reject the nullAs such, the final conclusion is that...There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 77.5.There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 77.5.The sample data support the claim that the population mean is not equal to 77.5.There is not sufficient sample evidence to support the claim that the population mean is not equal to 77.5.

Given information M= 70.5 n = 16 Standard deviation σ = 18.6 Hypothesis Null Hypothesis: H0:µ = 77.5…

Answered: You wish to test the following claim…

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 13PPS

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You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

Ho:μ=77.5Ho:μ=77.5
Ha:μ≠77.5Ha:μ≠77.5

You believe the population is normally distributed and you know the standard deviation is σ=18.6σ=18.6. You obtain a sample mean of M=70.5M=70.5 for a sample of size n=16n=16.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

in the critical region
not in the critical region

This test statistic leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 77.5.
There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 77.5.
The sample data support the claim that the population mean is not equal to 77.5.
There is not sufficient sample evidence to support the claim that the population mean is not equal to 77.5.

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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