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

Answer:

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

Step-by-step 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:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} } = 3.2$

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