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 1.45 cups per day and 1.56 cups per day for those drinking decaffeinated coffee. A random sample of 47 regular-coffee drinkers showed a mean of 4.42 cups per day. A sample of 37 decaffeinated-coffee drinkers showed a mean of 4.93 cups per day.

---Us the .0025 sig level---

a.This is a (Click to select)t

wo or one-tailed test.

b.The decision rule is

to reject H0 if Z < . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

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

d. What is your decision regardin H0?

reject/do not reject

5. the p value is ___

Explanation / Answer

(1) It is a one-tailed test

(2) Given a=0.01, the critical value is Z(0.01)= -2.33 (from standard normal table)

(3) The test statistic is

Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(4.3-4.89)/sqrt(1.45^2/51+1.59^2/47)

=-1.91

(4) Do not reject Ho.

(5) The p-value= P(Z<-1.91) =0.0281 (from standard normal table)

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