Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.14.1 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 10401040 samples is 4.04.0 ppm. Assume a population standard deviation of 1.21.2. Does the data support the researcher's claim at the 0.020.02 level?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

Given that ,

= 4.1

= 4.0

= 1.2

n = 1040

( 1 ) The null and alternative hypothesis is ,

H0 :   = 4.0

Ha : > 4.0

( 2 ) This is the right tailed test .

Test statistic = z

= ( - ) / / n

= ( 4.0 - 4.1 ) / 1.2 / 1040

= -2.69

( 3 ) The test statistic = -2.69

p (Z > -2.69 ) = 1 - P ( Z < -2.69 )

= 1 - 0.0036

0.9964

( 4 ) P-value = 0.9964

( 5 ) = 0.02

0.9964 > 0.02

P-value >

( 6 ) Fail to reject the null hypothesis .