IMathAS-libretexts

To continue answering our original question, test the claim that the mean nickel diameter drawn by children from the low income group is larger than the mean nickel diameter drawn by children from the high income group. Test at the 0.01 significance level.

Recall that for the lower income group,

\displaystyle \overline{{x}}

= 22.825, s = 5.0428293848918, n=40 and for the high income group

\displaystyle \overline{{x}}

= 19.771428571429, s = 3.6225252346437, n=35. The population standard deviations are unknown and assumed unequal.

a) If we use

\displaystyle {L}

to denote the low income group and

\displaystyle {H}

to denote the high income group, identify the correct alternative hypothesis.

$\displaystyle {H}_{{1}}:{p}_{{L}}\lt{p}_{{H}}$
$\displaystyle {H}_{{1}}:\mu_{{L}}\gt\mu_{{H}}$
$\displaystyle {H}_{{1}}:{p}_{{L}}\ne{p}_{{H}}$
$\displaystyle {H}_{{1}}:\mu_{{L}}\lt\mu_{{H}}$
$\displaystyle {H}_{{1}}:{p}_{{L}}\gt{p}_{{H}}$
$\displaystyle {H}_{{1}}:\mu_{{L}}\ne\mu_{{H}}$

b) The test statistic value is:

c) Using the Traditional method, the critical value is:

d) Based on this, we

Reject $\displaystyle {H}_{{0}}$
Fail to reject $\displaystyle {H}_{{0}}$

e) Which means

There is sufficient evidence to warrant rejection of the claim
There is not sufficient evidence to support the claim
There is not sufficient evidence to warrant rejection of the claim
The sample data supports the claim

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\displaystyle