Question

A country 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:

Answer 1

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

Explanation:

We are given the following in the question:

Population mean, μ = 30 miles per hour

Sample mean,
`\bar{x}` = 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

`H_(0): \mu = 30\text{ miles per hour}\\H_A: \mu > 30\text{ miles per hour}`

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

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(s)/(√(n)) }`

Putting all the values, we have

`t_(stat) = \displaystyle(35 - 30)/((4.7)/(√(15)) ) = 4.120`

Now,
`t_(critical) \text{ at 0.01 level of significance, 14 degree of freedom } = 2.624`

Since,

`t_(stat) > t_(critical)`

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.