Font Paragraph 1. The average age for licensed drivers in a county is..-42.6,0 1
ID: 3366484 • Letter: F
Question
Font Paragraph 1. The average age for licensed drivers in a county is..-42.6,0 12. A county police officer was interested in whether the average age of those receiving parking tickets differed from that of the average age of the population. She obtained a sample of drivers receiving parking tickets. The ages for these drivers are listed below: [35pts total] Driver ages 41 37 17 59 69 48 19 Use the above data to perform a z-test using the six steps of hypothesis testing. a. Conduct Step 1 of a hypothesis test for this scenario by stating the populations, comparison distribution, and assumptions for the test you are to conduct. Be sure to discuss if each assumption is met or not. [8 pts] Null Ho 42.6 Alternate H-42.6 b. Conduct Step 2 of a hypothesis test for this scenario. Please state the null (H) and research (H:) hypotheses both in words and in notation [6pts] Note: Here are a few mathematical & symbols you may need: ,.+ Null H 42.6 Alternate H 42.6 Conduct Step 3 of a hypothesis test for this scenario by calculating the standard error. Please show your your calculation. [6pts)] Note: You can type your work by inserting an equation, or simply typing using parentheses 0 and brackets (1 c. d. Conduct Step 4 of a hypothesis test for this scenario using an ?-.05. Be sure to include a sketch of the z-distribution with your critical values.l6pts)Explanation / Answer
Given that,
mu = 42.6
sigma = 12
Here we have to do one sample z-test.
a) Assumptions for one sample z-test :
Random sampling from a defined population
Interval or ratio scale of measurement
Population is normally distributed
b) Test of hypothesis is,
H0 : mu = 42.6 Vs H1 : mu not= 42.6
where mu is population mean.
c) Standard error = sigma / sqrt(n)
For the given data,
standard error = sigma / sqrt(n)
where sigma is standard deviation = 19.13
n = 8
SE = 6.76
d) The test statistic is,
Z = (Xbar - mu) / SE
where Xbar is sample mean = 39
Z = (39 - 42.6) / 6.76 = -0.53
Now we have to find P-value for taking the decision.
We can find P-value in excel.
syntax:
=2*NORMSDIST(z)
where z is test statistic.
P-value = 0.5945
P-value > alpha (0.05)
Accept H0 at 5% level of significance.
COnclusion : There is not sufficient evidence to say that A country police officer was interested in the average age of those receiving parking tickets different from that of the average age of the population.