A coffee manufacturer is interested in whether the mean daily consumption of reg

Question

A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.36 cups per day and 1.51 cups per day for those drinking decaffeinated coffee. A random sample of 50 regular-coffee drinkers showed a mean of 4.28 cups per day. A sample of 43 decaffeinated-coffee drinkers showed a mean of 5.29 cups per day.

Use the .05 significance level.

1. This is a
(Click to select)
two
one
-tailed test.

2.

The decision rule is to reject H0: r d if z < _________. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

3.

The test statistic is z =________ . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

4. What is your decision regarding H0 ?


(Click to select)
Do not rejected.
Rejected.

5. The p-value is__________ .

Explanation / Answer

a) This is a one-tailed (left tailed ) test. Researcher wishes to find if mean daily consumption of regular coffee drinkers is less than that of decaffeinated coffee drinkers.

b) Ar alpha=0.05, the critical valu eof Z (left tailed) is -1.96. Reject H0: Z<-1.96.

c) Test statistic, z is as follows:

SigmaXbar-Xbar=sqrt [s1^2/N1-1+S2^2/N2-1]

=sqrt[1.36/50-1+1.51/43-1]

=0.25

Z=(X1bar-X2bar)/SigmaXbar-Xbar

=(4.28-5.29)/0.25

=-4.04

The test statistic fall sin critical region, therefore, reject null hypothesis to cocnclude that mean daily consumption of regular coffee drinkers is less than that of decaffeinated coffee drinkers.

p value :0.0000

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