You wish to test the following claim (Ha) at a significance level of =0.05 . Ho:

Question

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

.

Ho:1=2

Ha:1<2

You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal You obtain a sample of size n1=16

with a mean of ¯x1=90.4 and a standard deviation of s1=16.5 from the first population. You obtain a sample of size n2=15 with a mean of ¯x2=101 and a standard deviation of s2=8.1

from the second population.

What is the test statistic for this sample?

test statistic = Round to 3 decimal places.

What is the p-value for this sample? For this calculation, use .

p-value = Use Technology Round to 4 decimal places.

The p-value is...

less than (or equal to)

greater than

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.

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 < 0
(with pooled variances)

Hypothesis test results:

Hence,

Test statistic = -2.246

P - value = 0.0163

The p - value is less than (or equal to) .

This test statistic leads to a decision to reject the null.

As such, the final conclusion is that the sample data support the claim that the first population mean is less than the second population mean.

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