Question

Set up the null and alternative hypothesis, find the test statistic, reject or fail to reject the null hypothesis, and write a conclusion based off of your results.According to the American Community Survey, the mean travel time to work in Collin County, Texas , in 2008 was 27.3 minutes. The Department of Transportation reprogrammed all the traffic lights in Collin County in an attempt to reduce travel time. To determine if there is evidence that travel time has decreased as a result of the reprogramming, the Department of Transportation obtains a random sample of 2500 commuters, records their

Answer 1

travel time to work, and finds a sample mean of 27.0 minutes with a standard deviation of 8.5 mins. Does this result suggest that travel time has decreased at the 5% level of significance?

Answer 2

please show any work done

Answer 3

so far i know i have to plug this into my calc but i cant figure out how to get the μ value for it or the Ho value

Answer 4

mu* value

Answer 5

checking

Answer 6

now i just need to find the alternative hypothesis and find the test statistic

Answer 7

okay i think im starting to get Ho and Ha.
if you could walk me through the test statistic that would rock

Answer 8

$$

\Large {
Hypotheses:~\\~\\
H_o :\mu = \mu_o \\
H_a: \mu < \mu_o
\\~\\
test~statistic:~z = \frac{\bar x - \mu_0}{\sigma / \sqrt{n} }

\\~\\ Critical Value: Left~Tailed ~ -z_{\alpha}

}

$$

Answer 9

ty!

Answer 10

$$
\Large {
Hypotheses:~\\~\\
H_o :\mu = 27.3 \\
H_a: \mu < 27.3
\\~\\
test~statistic:~z = \frac{27- 27.3}{8.5 / \sqrt{2500} }= -1.7647

\\~\\ Critical Value~ Left~Tailed: ~ -z_{.05} = -1.645

}

$$