## Question 695:

1

Research questions

Is the average age greater than 40 and is there evidence that there is a difference in price based on Type.

For the first research question, a 1 sample t-test was used on the 80 ages.

The NULL hypothesis is that the mean age is not different than 40 : Ho: Î¼ = 40.

The alternative hypothesis is that the mean age is greater than 40. Ha: Î¼ > 40.

A directional (1-tailed) test will be used with the alpha of .05 to test the hypothesis.

The results of the 1-sample t-test are below:

95%

Lower

Variable   N     Mean   StDev  SE Mean    Bound     T      P

Age       80  42.1500  8.2171   0.9187  40.6209  2.34  0.011

We see that the p-value is less than .05 so we would reject the NULL hypothesis and conclude the average age is greater than 40.

For the second part of the research question, we will compare the average price by Type. A 2-sample (non-directional) t-test will be conducted with an alpha of .05 to test the hypothesis.

The NULL hypothesis is that the mean prices are not different: Ho: Î¼1 = Î¼2.

The alternative hypothesis is that the mean prices are different Ha: Î¼1 â Î¼2.

The results of the 2-sample t-test are below:

Two-Sample T-Test and CI: Price, Type

Two-sample T for Price

Type   N   Mean  StDev  SE Mean

0     30  25846   4289      783

1     50  21641   3594      508

Difference = mu (0) - mu (1)

Estimate for difference:  4204.86

95% CI for difference:  (2332.41, 6077.31)

T-Test of difference = 0 (vs not =): T-Value = 4.50  P-Value = 0.000  DF = 53

We see that the p-value is less than .05 (in fact it is less than .0001) so we would reject the NULL hypothesis and conclude there is a difference in price by Type.