Question

you want to test a claim that the mean amount of lead in the air of British cities is greater than .036 micrograms per cubic meter. In a sample random sample of 61 British cities you find that the sample mean of lead in the air is .039 micrograms per cubic meter and the sample standard deviation is .069 micrograms per cubic meter.Let α=.01 . Run a hypothesis test to test the claim. Use either a p-value or a rejection region to make your decision.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0.036

H_a : > 0.036

Test statistic = z

= ( - ) / s / n

= (0.039 - 0.036) / 0.069 / 61

Test statistic = 0.34

P(z > 0.34) = 1 - P(z < 0.34) = 0.3669

P-value = 0.3669

= 0.01

P-value >

Fail to reject the null hypothesis .

There is sufficient evidence that the mean amount of lead in the air of British cities is greater than .036

micrograms per cubic meter .