Answer:
(a) <em>H₀</em>: <em>μ</em> = 5 vs. <em>Hₐ</em>: <em>μ</em> ≠ 5.
(b) The test statistic value is -3.67.
(c) The <em>p</em>-value of the test is 0.0025.
(d) The mean amount of time spent in the shower by an adult is different from 5 minutes.
Step-by-step explanation:
In this case we need to test whether the mean amount of time that college students spend in the shower is significantly different from 5 minutes.
The information provided is:
(a)
The hypothesis for the test can be defined as follows:
<em>H₀</em>: The mean amount of time spent in the shower by an adult is 5 minutes, i.e. <em>μ</em> = 5.
<em>Hₐ</em>: The mean amount of time spent in the shower by an adult is different from 5 minutes, i.e. <em>μ</em> ≠ 5.
(b)
As the population standard deviation is not known we will use a <em>t</em>-test for single mean.
Compute the test statistic value as follows:
Thus, the test statistic value is -3.67.
(c)
Compute the <em>p</em>-value of the test as follows:
*Use a <em>t</em>-table.
Thus, the <em>p</em>-value of the test is 0.0025.
(d)
Decision rule:
If the <em>p</em>-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
<em>p</em>-value = 0.0025 < <em>α</em> = 0.01
The null hypothesis will be rejected at 1% level of significance.
Thus, concluding that the mean amount of time spent in the shower by an adult is different from 5 minutes.