For the next, complete the next steps one by one: 1-State the null hypothesis an
ID: 3133860 • Letter: F
Question
For the next, complete the next steps one by one:
1-State the null hypothesis and the alternate hypothesis
2-Select the level of significance
3-Determine the test statistics and graph it (tail test)
4-Formulate a decision rule
5-Make the decision regarding the Ho and interpret the result.
The following observations show the number of traffic violations given for speeding on the one interstate highway going through Smallville by Officers Dhondt and Meridith of the Police Department over the last 5 months:
Dhondt 30 22 25 19 26
Meridith 26 19 20 15 19
At the .05 level of significance, is there a difference in the mean number of citations given by the two officers? Assume the population of differences is normal.
Explanation / Answer
The differences are
-4
-3
-5
-4
-7
Formulating the null and alternative hypotheses,
Ho: ud = 0
Ha: ud =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the standard deviation of the differences
s = 2.539088359
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 1.135514835
Calculating the mean of the differences
XD = -4.6
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = -4.051025896
As df = n - 1 = 4
Then the critical value of t is
tcrit = +/- 2.776445105
Also, using p values,
p = 0.015462635
As |t| > 2.776, and P < 0.05, WE REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that the mean number of citations given by the two officers are different at 0.05 level. [CONCLUSION]