Question

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let μ denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: μ = 20 versus Ha: μ > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.) (a) n = 13, t = 3.2, α = 0.05

Answer 1

We conclude that average reflectometer reading for a new type of paint is greater than 20

Explanation:

We are given the following in the question:

Population mean, μ = 20

Sample size, n = 13

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

`H_(0): \mu = 20\\H_A: \mu > 20`

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) } = 3.2`

Degree of freedom = n - 1 = 13 - 1 = 12

Now, we calculate the p-value with the help of standard table.

P-value = 0.004

Since, the p-value is less than the significance level, we fail to accept the null hypothesis and reject it.

Thus, there is enough evidence to support that average reflectometer reading for a new type of paint is greater than 20