Question

A city is concerned that cars are not obeying school zones by speeding through them, putting children at greater

risk of injury. The speed limit in school zones is 15 miles per hour. Throughout the course of one day, a police officer
hides his car on a side street that intersects the middle of the school zone and records the speed of each car that
passes through. The 36 cars that he recorded had an average speed of 16.33 mph with a sample standard deviation
of 2.54 mph.
Calculate the appropriate test statistic (Give as a decimal rounded to the nearest thousandth).

Answer 1

Answer: test statistic = 0.002

Explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 15

For the alternative hypothesis,

µ > 15

The inequality sign means that it is right tailed.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 36,

Degrees of freedom, df = n - 1 = 36 - 1 = 35

t = (x - µ)/(s/√n)

Where

x = sample mean = 16.33

µ = population mean = 15

s = samples standard deviation = 2.54

t = (16.33 - 15)/(2.54/√36) = 3.14

We would determine the p value using the t test calculator. It becomes

p = 0.002