Need help with the four step process.

Question

Radon is a colorless, odorless, invisible gas that seeps into residential homes and has been linked to lung cancer. A generally acceptable safe level of radon is 4 pCi/L. A random sample of 32 homes in a certain county in West Virginia was obtained and the radon level in each was carefully measured. The sample mean was 𝑥̅=4.9 with a standard deviation of s = 2.1.

Do the four step process

State:

Formulate:

Solve:

Conclude:

Answer 1

State:

Ho: mu = 4

Ha: mu > 4 (radon level unsafe)

parameter is acceptably safe radon level

not given significance level, so will assume significance level (alpha)= 0.05.

Formulate: will do a one-sample t-test. random sample, large sample size (> 30) and sample size less than 10% of the population

Solve: t-stat = (sample mean - population mean)/(sample standard deviation/square root(sample size) =

(4.9 - 4)/(2.1/sqrt(32)) = 2.42

p-value = P(t > 2.42) with 31 degrees of freedom is just above 0.1 (use table value for DOF = 30).

Do not reject Ho at 0.05 level of significance as p-value > level of significance.

Conclude: We do not have sufficient evidence that the level of radon in the county in West Virginia is unsafe at the 0.05 level of significance.