Question

1. Suppose you would like to know the average daily number of car crashes that occur at your hometown.  With that in mind, you take a sample of 15 days where you record the number of car crashes at your hometown on each of those days.  The data are displayed below: 12,  7,  17,  11,  9,  8,  19,  22,  12,  17,  15,  9,  12,  21, 15

a)  Please calculate the sample average.

b)  Please calculate the standard error of the sample average.  (Please make sure to show your calculations.)

c)  Your friend claims that the population average (mean) for the daily number of car crashes at your hometown is 11.2.  Using your sample data, please test your friend’s hypothesis using a significance level of 4%.  In other words, do you “reject” or “fail to reject” your boss’ null hypothesis at the 4% significance level?  Please use both the t-stat method and the p-value method.

Answer 1

Given:

The given data x = 12,  7,  17,  11,  9,  8,  19,  22,  12,  17,  15,  9,  12,  21, 15

a) The sample average :

So the standard error is SE = 1.2207

c) Claims : The population average (mean) for the daily number of car crashes at your hometown is 11.2.  

Hypothesis test:

The null and alternative hypothesis is

Ho : = 11.2

Ha : 11.2

Using P-value approach :

P-value corresponding to t = 2.073 with df = 14 is

P-value = 2 P(t>2.073) = 0.0571

Since P-value > = 0.04, we fail to reject null hypothesis

Decision : Fail to reject null hypothesis.

Conclusion : There is not sufficient evidence to conclude that the population average (mean) for the daily number of car crashes at your hometown is 11.2.