Answer:
1. Null Hypothesis, :
70 mph
Alternate Hypothesis<u>,</u> :
> 70 mph
2. Value of test statistics is 2.652.
Step-by-step explanation:
We are given that Kansas Highway Patrol recorded the speed of 450 interstate vehicles and found the mean speed of 70.2 mph with standard deviation 1.6 mph.
We have to conduct a hypothesis test at significance level 0.01 to decide whether or not to reduce the money sent to Kansas.
<em><u>Let </u></em><em><u> = true mean speed of all vehicles on the Kansas interstate highway system.</u></em>
SO, <u>Null Hypothesis</u>, :
70 mph {means that the federal government will not reduce the amount of funding it provides as the speed limit is less than or equal to 70 mph}
<u>Alternate Hypothesis,</u> :
> 70 mph {means that the federal government will reduce the amount of funding it provides as the speed limit exceed 70 mph}
The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean speed limit of 450 interstate vehicles = 70.2 mph
s = sample standard deviation = 1.6 mph
n = sample of vehicles = 450
So, <em><u>test statistics</u></em> = ~
= 2.652
<u><em>Hence, the value of test statistics is 2.652.</em></u>