Question

A researcher shows that a person averages $380 a month on gas for their vehicles with a population standard deviation of $42. there were 38 randomly sampled.

A second researcher claims the actual money spent is less than $350.

-What is the null hypothesis?

-What is the alternative hypothesis?

-What kind of test are we looking at?? One tail, Two tail, Both, or Neither?

-What is the critical value? (Round to the nearest thousandth)

-Would you reject the null hypothesis or fail to reject the null hypothesis?

-Is there sufficient evidence to support the claim?

Answer 1

a) As we are testing here whether the mean is less than 350, therefore the null and the alternative hypothesis here are given as:

b) As we are testing it from lower side only, therefore this is a one tailed test that is a left tailed test here.

c) For 0.05 level of significance, we have from the standard normal tables:
P( Z < -1.645) = 0.05

Therefore -1.645 is the critical value here.

d) The test statistic here is computed as:

As the critical value here is 4.40 > -1.645, therefore it lies in the non rejection region here. Therefore we fail to reject the null hypothesis here.

e) As the test is not significant, therefore we dont have sufficient evidence here that the mean is not less than 350 here.