You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:μ=61.4Ho:μ=61.4 Ha:μ<61.4Ha:μ<61.4You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=108n=108 with mean M=59.7M=59.7 and a standard deviation of SD=10.2SD=10.2.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is...less than (or equal to) ααgreater than ααThis 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 less than 61.4.There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 61.4.The sample data support the claim that the population mean is less than 61.4.There is not sufficient sample evidence to support the claim that the population mean is less than 61.4.

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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

Section10.4: Distributions Of Data

Problem 19PFA

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Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.

Ho:μ=61.4Ho:μ=61.4
Ha:μ<61.4Ha:μ<61.4

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=108n=108 with mean M=59.7M=59.7 and a standard deviation of SD=10.2SD=10.2.

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

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

less than (or equal to) αα
greater than αα

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 less than 61.4.
There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 61.4.
The sample data support the claim that the population mean is less than 61.4.
There is not sufficient sample evidence to support the claim that the population mean is less than 61.4.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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