Question

Test a claim that the mean amount of lead in the US the standard deviation is 0.065 microgram per cubic meter. At is than 0.03 0.10, can then gram per te m it was found that the amount of the afore be suported Complete t h e bow. Assume the population is m m is 0.038 microgram per cubic meland y ample of S4US. bed a) Identify them and Hand HD (Typengers or decimal Dentround) Themishe hypothesis (h) Find the article ) and identify the Theorical value() are Use a conna to separate an d region Round to w ipes ded)

Answer 1

Given that the population is normal with a claim that the population mean $\mu$ is less than 0.036. for the claim a sample of 54 is taken into consideration which results in sample mean $\bar{X}$=0.038 and sample standard deviation s=0.068 so, the hypotheses are:

(a)

Ho: u = 0.036

Hα μ U.036

Based on the hypothesis the claim is the alternate hypothesis.

b) At 0.10 level of significance and degree of freedom=n-1=54-1=53 the critical region for a left tail test is calculated using excel formula =T.INV(0.1,53)

The critical value is -1.30.

The rejection region in graph is :

-1 t=-1,3

t<to=-1.30

c) Test statistic:

The test statistic is calculated as:

0.038 – 0.036 = 0.216 %3D 0.068/V54 s/Vn

t=0.22

d) Decision:

Since t>to Do not reject the null hypothesis because the test statistic does not lie in the rejection region.

e) Conclusion:

Since we do not reject the null hypothesis hence There is not enough evidence at a 10% level of significance to support the claim that the mean amount of lead in the air in US cities is less than 0.036 microgram per cubic meter.