A new community safety education and outreach intervention is introduced in Bios

Question

A new community safety education and outreach intervention is introduced in Biostats-ville, designed to lower the number of motor vehicle accidents occurring in that community. After 8 years of implementation, the average number of reported motor vehicle accidents per month (n=96) is recorded to be 85. Researchers know the general population average number of motor vehicle accidents per month from all communities of a similar size is 87 with a standard deviation of 8.5.

Use the data above examining the research question of interest: "Does Biostats-ville (with the new community safety education and outreach intervention) have a different average number of reported motor vehicle accidents per month than the population average of communities of a similar size?"

What is the p-value associated with your test statistic? (rounded to the nearest ten thousandth)

*Hint: remember what type of test you are conducting (one-tailed vs. two-tailed).

Explanation / Answer

Solution:

Here, we have to use one sample z test for population mean.

Null hypothesis: H0: Biostats-ville (with the new community safety education and outreach intervention) has a same average number of reported motor vehicle accidents per month than the population average of communities of a similar size.

Alternative hypothesis: Ha: Biostats-ville (with the new community safety education and outreach intervention) has a different average number of reported motor vehicle accidents per month than the population average of communities of a similar size.

H0: µ = 87 vs. Ha: µ ? 87

This is a two tailed test.

We are given

Sample size = n = 96

Sample mean = Xbar = 85

Population standard deviation = ? = 8.5

Test statistic is given as below:

Z = (Xbar - µ) / [?/sqrt(n)]

Z = (85 – 87) / [8.5/sqrt(96)]

Z = -2/ 0.867528

Z = -2.3054

P-value = 0.0214

(By using z-table)

Required Answer: 0.0214

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