You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1<μ2Ha:μ1<μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=20n1=20 with a mean of M1=78.9M1=78.9 and a standard deviation of SD1=17.6SD1=17.6 from the first population. You obtain a sample of size n2=18n2=18 with a mean of M2=93.6M2=93.6 and a standard deviation of SD2=8.8SD2=8.8 from the second population.What is the p-value for this test? For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (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 first population mean is less than the second population mean. There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean. The sample data support the claim that the first population mean is less than the second population mean. There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

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

Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1<μ2Ha:μ1<μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=20n1=20 with a mean of M1=78.9M1=78.9 and a standard deviation of SD1=17.6SD1=17.6 from the first population. You obtain a sample of size n2=18n2=18 with a mean of M2=93.6M2=93.6 and a standard deviation of SD2=8.8SD2=8.8 from the second population.

What is the p-value for this test? For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (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 first population mean is less than the second population mean.
There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
The sample data support the claim that the first population mean is less than the second population mean.
There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

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