Question 1 8 points Suppose that you want to test the claim

Question 1     (8 points)

Suppose that you want to test the claim that the mean weight of the giant Pacific octopus is 40 pounds or less. You collect a sample of 90 octopuses and find that the mean weight in the sample is 41 pounds. The standard deviation is 4 pounds.

Part (a)                        (2 points)

Given that the average in the sample is more than what is claimed in the null hypothesis, explain why it is still necessary to carry out a hypothesis test to test the claim.

Part (b)            (4 points)

Using a level of significance of 0.05, test the null hypothesis H₀: µ40 using the 6-step procedure.

H₀: µ40   H₀: µ>40

Part (c)                        (2 points)

Using a level of significance of 0.05, test the null hypothesis H₀: µ40 using the p-value.

(Reminder: Your decision whether to reject or not reject H₀ will be the same with the 6-step procedure and the p-value, but you must show how you arrive at that conclusion.)

Solution

a) In hypothesis testing procedure, we use the results obtained for the entire population. So we cannot assume the mean to be lesser based on just one sample. Hence to extrapolate the result to the entire population it is required to carryout hypothesis testing.

b) H0: mu<=40

H1: mu>40

Z=xbar-mu/s/sqrt(n)

xbar=41, mu=40, s=4,n=90

z=2.37

the critcal value is 1.645.

As z > 1.645, we reject the nul hypothesis.

So the conclusion is that mu>40

c) to get p value use this function NORM.S.DIST(2.37,TRUE) in excel and subtract with one. So p value is 0.0089. So decision is as above.