Acountry is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour. a random sample of 15 vehicles has a mean speed of 35 miles per hour and a standard deviation of 4.7 miles per hour. at ? = .01, do you have enough evidence to supprot the country's claim?

calculate the p-value:

We conclude that speed is greater than 30 miles per hour.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ =  30 miles per hour

Sample mean, = 35 miles per hour

Sample size, n = 15

Alpha, α = 0.01

Sample standard deviation, s = 4.7 miles per hour

First, we design the null and the alternate hypothesis

We use one-tailed(right) t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,                  

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis and conclude that speed is greater than 30 miles per hour.

We calculate the p-value.

P-value = 0.00052

Since p value is lower than the significance level, we reject the null hypothesis and accept the alternate hypothesis. We conclude that speed is greater than 30 miles per hour.

step-by-step explanation: