1. You wish to test the following claim (H1) at a significance level of α=0.005 Ho:μ=51.4 H1:μ>51.4You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=794 with mean ¯x=52.2 and a standard deviation of s=16.7What is the test statistic for this sample? (Report answer accurate to four 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 greater than 51.4.There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 51.4.The sample data support the claim that the population mean is greater than 51.4.There is not sufficient sample evidence to support the claim that the population mean is greater than 51.4. 2. You wish to test the following claim (H1) at a significance level of α=0.001 Ho:μ=68.4 H1:μ>68.4You believe the population is normally distributed and you know the standard deviation is σ=15.3. You obtain a sample mean of M=73.3M for a sample of size n=71.What is the critical value for this test? (Report answer accurate to four decimal places.)critical value = What is the test statistic for this sample? (Report answer accurate to four 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 greater than 68.4.There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 68.4.The sample data support the claim that the population mean is greater than 68.4.There is not sufficient sample evidence to support the claim that the population mean is greater than 68.4.

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Answered: You wish to test the following claim…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. You wish to test the following claim (H1) at a significance level of α=0.005

Ho:μ=51.4
H1:μ>51.4

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=794 with mean ¯x=52.2 and a standard deviation of s=16.7

What is the test statistic for this sample? (Report answer accurate to four 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 greater than 51.4.
There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 51.4.
The sample data support the claim that the population mean is greater than 51.4.
There is not sufficient sample evidence to support the claim that the population mean is greater than 51.4.

2. You wish to test the following claim (H1) at a significance level of α=0.001

Ho:μ=68.4
H1:μ>68.4

You believe the population is normally distributed and you know the standard deviation is σ=15.3. You obtain a sample mean of M=73.3M for a sample of size n=71.

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

What is the test statistic for this sample? (Report answer accurate to four 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 greater than 68.4.
There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 68.4.
The sample data support the claim that the population mean is greater than 68.4.
There is not sufficient sample evidence to support the claim that the population mean is greater than 68.4.

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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