Question

Statistics: Hypothesis Testing

Answer 1

Answer:

Yes, the data supports the claim that the aluminum bottle cools faster.

Step-by-step explanation:

When doing a hypothesis test, remember the acronym PHANTOMS.

P (p definition)

let $p_{glass}$ = the mean time that the clear glass bottles take to chill from 75F to 45F

let $p_{aluminum}$ = the mean time that the aluminum bottles take to chill from 75F to 45F

H (hypotheses)

$H_{0}$ is $p_{aluminum} = p_{glass}$

$H_{a}$ is $p_{aluminum} < p_{glass}$

A (assumptions)

There is no evidence that these bottles were picked randomly or independently, but we'll solve as if they were. Both samples are larger than 30, so we can assume the distribution will be close to normal.

N (name the test)

Because the above assumptions are met, we can perform an independent samples t-test. We will use an alpha level of 0.05.

T (test)

$t = \frac{\overline{x_{aluminum}} - \overline{x_{glass}}}{\sqrt{\frac{S_{aluminum}^{2} }{n_{aluminum}} + {\frac{S_{glass}^{2} }{n_{glass}}}}}$

t = $\frac{92.4 - 133.8}{\sqrt{\frac{7.3^{2} }{35} - \frac{9.9^{2} }{42}}}$

t = -21.08

O (obtain p-value)

In a graphing calculator, go to stat → tests → 2 samp T test → and enter the given data (select not pooled).

p-value = 0

M (make a decision)

Because the p-value is less than 0.05, I will reject the null hypothesis.

S (state your conclusion)

There is significant evidence to support the claim that the aluminum bottle does cool faster than the traditional glass bottle.