Respuesta :
Answer:
The mean commute time in the U.S. is less than half an hour.
Step-by-step explanation:
In this case we need to test whether the mean commute time in the U.S. is less than half an hour.
The information provided is:
[tex]n=45\\\bar x=25.5\\s=19.1\\\alpha =0.05[/tex]
(a)
The hypothesis for the test can be defined as follows:
H₀: The mean commute time in the U.S. is not less than half an hour, i.e. μ ≥ 30.
Hₐ: The mean commute time in the U.S. is less than half an hour, i.e. μ < 30.
(b)
As the population standard deviation is not known we will use a t-test for single mean.
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{25.2-30}{19.1/\sqrt{45}}=-1.58[/tex]
Thus, the test statistic value is -1.58.
(c)
Compute the p-value of the test as follows:
[tex]p-value=P(t_{(n-1)}<-1.58)=P(t_{(45-1)}<-1.58)=0.061[/tex]
*Use a t-table.
The p-value of the test is 0.061.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.061> α = 0.05
The null hypothesis will not be rejected at 5% level of significance.
Thus, concluding that the mean commute time in the U.S. is less than half an hour.
