IMathAS-libretexts

You wish to test the following claim (

\displaystyle {H}_{{a}}

) at a significance level of

\displaystyle \alpha={0.10}

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

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

You obtain a sample of size

\displaystyle {n}_{{1}}={7}

with a mean of

\displaystyle \overline{{x}}_{{1}}={64.8}

and a standard deviation of

\displaystyle {s}_{{1}}={10.4}

from the first population. You obtain a sample of size

\displaystyle {n}_{{2}}={6}

with a mean of

\displaystyle \overline{{x}}_{{2}}={69.6}

and a standard deviation of

\displaystyle {s}_{{2}}={8.9}

from the second population.

Find a confidence interval for the difference of the population means. For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (Report answer accurate to three decimal places.)
confidence interval =

The test statistic is...

the confidence interval contains zero
all values in the confidence interval are below zero
all values in the confidence interval are above zero

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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