Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.0 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 21 samples is 6.3 ppm with a standard deviation of 1.1. Does the data support the claim at the 0.025 level? Assume the population distribution is approximately normal.

(a) Find the value of the test statistic. (b) Round your answer to three decimal places. (c) Specify if the test is one-tailed or two-tailed.(d) Determine the decision rule for rejecting the null hypothesis.(e) Make the decision to reject or fail to reject the null hypothesis

Answer 1

Solution :

= 6.0

= 6.3

s = 1.1

n = 21

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 6.0

Ha : > 6.0

Test statistic = t

= ( - ) / s / n

= (6.3 - 6.0) / 1.1 / 21

= 1.250

p(t >1.250 ) = 1-P (t< 1.250) = 0.1125

P-value = 0.1125

= 0.025  

0.1125 >0.025

Do not reject the null hypothesis .

There is insufficient evidence to suggest that