Please go over all the steps and explain them clearly for me. I want to understa
ID: 3262773 • Letter: P
Question
Please go over all the steps and explain them clearly for me. I want to understand.
The U.S. government provides money to each state to maintain the interstate highway system in the state. The U.S. can revoke or reduce the money if the states do not safely maintain the highways. The U.S. government is particularly concerned about the speed of traffic on Kansas highways. If the average speed of all interstate highway vehicles in Kansas exceeds the posted speed limit of 70 mph, the federal government will reduce the amount of funding it provides. 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. The U.S. government will use this information to conduct a hypothesis test at significance level 0.01 to decide whether or not to reduce to money sent to Kansas.
Suppose that mu is the true mean speed of all vehicles on the Kansas interstate highway system.
What are the null and alternative hypotheses that the U.S. government should test?
What is the value of the test statistic?
What is the rejection region?
Do we reject the null hypothesis?
Based on this hypothesis test, will the U.S. government reduce the money sent to Kansas?
Should the p-value for this test be greater than or less than the significance level?
Calculate the p-value for this test.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 70
Alternative hypothesis: > 70
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.075425
DF = n - 1 = 450 - 1
D.F = 449
t = (x - ) / SE
t = 2.65
tcritical = 2.587
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Thus the P-value in this analysis is 0.0043
Interpret results. Since the P-value (0.0043) is less than the significance level (0.01), we have to reject the null hypothesis.
Yes, U.S. government should reduce the money sent to Kansas.