Question

5. A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci.

a) In testing the scientist's belief, write the appropriate hypotheses:

            H_o: μ <= 4                  H_a:

b) What decision should be made?

	___crit =                                 α =                                                                                     __stat =                                pvalue =

Answer 1

a)
H0: <= 4 , Ha: ​​​​ > 4

b)

df = n - 1 = 36 - 1 = 35

= 0.05

t crit at 0.05 significance level with 35 df = 1.690

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 4.4 - 4) / ( 1 / sqrt( 36) )

= 2.4

From T table,

With test statistics of 2.4 and df of 35 ,

p-value (one tailed) = 0.0109

Since p-value < 0.05 , Reject the null hypothesis