Question

In: Statistics and Probability

Businesses, particularly those in the food preparation industry such as General Mills, Kellogg, and Betty Crocker...

Businesses, particularly those in the food preparation industry such as General Mills, Kellogg, and Betty Crocker regularly use coupons to stimulate their sales. There is concern that users of paper coupons (Population p) are different from users of e-coupons (Population e). One survey recorded the age of each person who redeemed a coupon along with the type (either electronic or paper). The sample of 29 e-coupon users had a mean age of 36.1 years with a sample standard deviation of 11.2, while a similar sample of 22 paper-coupon users had a mean age of 40.6 with a sample standard deviation of 5.0.

(1)

Find the degrees of freedom for unequal variance test. (Round down your answer to next lower whole number.)
  Degrees of freedom:   
(2)

State the decision rule for 0.01 significance level: H0: μe = μp; H1: μe ≠ μp. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)
  Reject H0 if t < ? or t > ?
(3)

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign.  Carry at least 3 decimal places in intermediate calculations.  Round your answer to 2 decimal places.)
  Value of the test statistic:   
(4)

Test the hypothesis of no difference in the mean ages of the two groups of coupon users. Use the .01 significance level.
(Reject or Do not reject)H0? There is a (significant no significant) difference in the mean ages of the two groups of coupon users.

Solutions

Expert Solution

Solution: We can use the TI-84 to find the answer to the given questions. The steps to be followed are:

Press STAT and then scroll right to TESTS

Scroll down to 2-SampTTest and scroll right to Stats

Enter the values as:

The output is:

(1) Find the degrees of freedom for unequal variance test.

Answer:

(2) State the decision rule for 0.01 significance level: H0: μe = μp; H1: μe ≠ μp.

Answer: Reject H0 if t < - 2.701 or t > 2.701

(3) Compute the value of the test statistic.

Answer:

(4)  Test the hypothesis of no difference in the mean ages of the two groups of coupon users. Use the .01 significance level.

Answer: Do not reject H0. There is no significant difference in the mean ages of the two groups of coupon users.

orchestra answered 2 years ago
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