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. For a significance level of α = 0.05, do we reject the null hypothesis? Which of the following is an appropriate conclusion?

If we compare the p value and the significance level given and we can see that so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the true average speed is lower than 25 mph at 5% of signficance.  

Step-by-step explanation:

Data given and notation  

represent the sample mean

represent the sample standard deviation

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean for the average speed is lower than 25 mph, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

 (1)  

Calculate the statistic

We can replace in formula (1) the info given like this:  

P-value

The first step is calculate the degrees of freedom, on this case:  

Since is a one side test the p value would be:  

Conclusion  

If we compare the p value and the significance level given and we can see that so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the true average speed is lower than 25 mph at 5% of signficance.  

a: 1/6, j: 1/4

step-by-step explanation: you are welcome

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.