Question

A safety officer wants to prove that μ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Assume that the speeds of cars are normally distributed. What is the p-value?

Answer 1

Answer:

$t=\frac{24-25}{\frac{2.2}{\sqrt{14}}}=-1.70$    

The degrees of freedom are given by:

$df=n-1=14-1=13$  

The p value for this case would be given by:

$p_v =P(t_{(13)}$  

Step-by-step explanation:

Information given

$\bar X=24$ represent the mean height for the sample  

$s=2.2$ represent the sample standard deviation

$n=14$ sample size  

$\mu_o =25$ represent the value that we want to test

t would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to verify

We want to cehck if the true mean is lees than 25 mph, the system of hypothesis would be:  

Null hypothesis:$\mu \geq 25$  

Alternative hypothesis:$\mu < 25$  

The statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$  (1)  

Replacing the info given we got:

$t=\frac{24-25}{\frac{2.2}{\sqrt{14}}}=-1.70$    

The degrees of freedom are given by:

$df=n-1=14-1=13$  

The p value for this case would be given by:

$p_v =P(t_{(13)}$