It is advertised that the average braking distance for a small car traveling at 75 miles per hour equals 124 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 37 small cars at 75 miles per hour and records the braking distance. The sample average braking distance is computed as 112 feet. Assume that the population standard deviation is 22 feet.

Since the p value is a very small value at any significance level used we can reject the null hypothesis and we can conclude that the true mean for this case is different from 124 ft

Step-by-step explanation:

Data given and notation

[tex]\bar X=112[/tex] represent the sample mean

[tex]\sigma =22[/tex] represent the population standard deviation

[tex]n=37[/tex] sample size

[tex]\mu_o =124[/tex] represent the value that we want to test

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to check the following system of hypothesis:

Null hypothesis: [tex]\mu = 124[/tex]

Alternative hypothesis :[tex]\mu \neq 124[/tex]

The statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)

Replacing the info given we got:

[tex]z=\frac{112-124}{\frac{22}{\sqrt{37}}}=-3.318[/tex]

The p value would be given by this probability:

[tex]p_v =2*P(z<-3.318)=0.0009[/tex]

Since the p value is a very small value at any significance level used we can reject the null hypothesis and we can conclude that the true mean for this case is different from 124 ft