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 1.21 cups per day and 1.40 cups per day for those drinking decaffeinated coffee. A random sample of 54 regular-coffee drinkers showed a mean of 4.59 cups per day. A sample of 49 decaffeinated-coffee drinkers showed a mean of 5.64 cups per day. Use the 0.100 significance level. a) Is this a one tailed or two tailed test? b) State the decision rule. c) Compute the value of the test statistic. d) What is the P-value? e) What is your decision about Ho?

Answer 1

Let mean of regular-coffee drinkers = 1 and Mean of decaffeinated-coffee drinkers = 2

a)

H0: 1 >= 2

Ha: 1 < 2

This is one tailed test.

b)

From Z table, z critical value at 0.100 significance level = -1.2816

Decision rule = Reject H0 if z < -1.2816

c)

Test statistics

z = ( 1 - 2 ) / sqrt [ 1 / n1 + 2 / n2 ]

= (4.59 - 5.64 ) / sqrt [ 1.212 / 54 + 1.402 / 49 ]

= -4.05

d)

p-value = P(Z < z)

= P(Z < -4.05)

= 0 (From Z table)

e)

Since test statistics falls in rejection region, Reject the null hypothesis