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 1.37 cups per day and 1.47 cups per day for those drinking decaffeinated coffee. A random sample of 47 regular-coffee drinkers showed a mean of 4.39 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.78 cups per day. Use the 0.01 significance level. Is this a one-tailed or a two-tailed test? One-tailed test. Two-tailed test. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is the p-value? What is your decision regarding H0? Reject H0. Do not reject H0. rev: 10_12_2017_QC_CS-102203, 11_21_2017_QC_CS-110078

Explanation / Answer

Sol:

Null hypothesis:

Ho:

mean(regular coffee)=mean(decaffeinated coffee)

Alternative Hypothesis:

Ha:

mean(regular coffee)<mean(decaffeinated coffee)

Its a one tail tailed test.

alpha=0.01

decision rule:

if p<0.01 reject null hypothesis.

if p>0.01 fail to reject null hypothesis.

test statistc:

t=x1 bar-x2 bar/sqrt(s1^2/n1+s2^2/n2)

=4.39-5.78/sqrt(1.37^2/47+1.47^2/40)

=-4.53

t=-4.53

the value of the test statistic=-4.53

df=n1+n2-2=85

p=0.0000

p<0.00001

Reject Null hypothesis

Reject H0.

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