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 1.39 cups per day and 1.55 cups per day for those drinking decaffeinated coffee. A random sample of 45 regular-coffee drinkers showed a mean of 4.59 cups per day. A sample of 39 decaffeinated-coffee drinkers showed a mean of 5.19 cups per day.

Use the 0.050 significance level.

1. Is this a one-tailed or a two-tailed test?

• One-tailed test.

• Two-tailed test.

2. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

4. What is the p-value?

5. What is your decision regarding H₀?

• Reject H₀.

• Do not reject H₀.

Answer 1

Let , be the population mean daily consumption of regular-coffee drinkers and   be the population mean daily consumption of decaffeinated-coffee drinkers.

The null and alternative hypothesis is ,

Since , the population standard deviations are known.

Therefore , use normal distribution.

a. The test is one tailed test.

b. The critical value is ,

The decision rule is , Reject Ho , if Z-stat<-1.64

c. The value of the test statistic is ,

d. The p-value is ,

p-value=

; From standard normal distribution table

e. Decision : Here , p-value=0.0314<0.050

Thererfore , reject Ho.

COnclusion : Hence , there is sufficient evidence to support the claim that the the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers.