IMathAS-libretexts

You wish to test the following claim (

\displaystyle {H}_{{a}}

) at a significance level of

\displaystyle \alpha={0.05}

\displaystyle {H}_{{o}}:\mu_{{1}}=\mu_{{2}}

\displaystyle {H}_{{a}}:\mu_{{1}}\ne\mu_{{2}}

You believe both populations are normally distributed, but you do not know the standard deviations for either. You should use a non-pooled test. You obtain a sample of size

\displaystyle {n}_{{1}}={27}

with a mean of

\displaystyle {M}_{{1}}={84.8}

and a standard deviation of

\displaystyle {S}{D}_{{1}}={10.9}

from the first population. You obtain a sample of size

\displaystyle {n}_{{2}}={12}

with a mean of

\displaystyle {M}_{{2}}={74.8}

and a standard deviation of

\displaystyle {S}{D}_{{2}}={20.3}

from the second population.

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? 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) $\displaystyle \alpha$
greater than $\displaystyle \alpha$

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

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