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The null and alternate hypotheses are:

*H*_{0} : *? _{d}* ? 0

The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of 4 days last month.

Day | ||||

1 | 2 | 3 | 4 | |

Day shift | 9 | 12 | 14 | 18 |

Afternoon shift | 7 | 8 | 11 | 14 |

At the 0.05 significance level, is there a difference in the mean number of citations given by the two shifts?

**Required:
a. **What is the

P-value............???

Businesses such as General Mills, Kellogg's, and Betty Crocker regularly use coupons to build brand allegiance and stimulate sales. Marketers believe that the users of paper coupons are different from the users of e-coupons accessed through the Internet. One survey recorded the age of each person who redeemed a coupon along with the type of coupon (either paper or electronic). The sample of 22 traditional paper-coupon clippers had a mean age of 42.0 with a standard deviation of 5.0. The sample of 35 e-coupon users had a mean age of 35.2 years with a standard deviation of 8.8. Assume the population standard deviations are not the same. Using a significance level of 0.05, test the hypothesis of no difference in the mean ages of the two groups of coupon clients. *Hint*: For the calculations, assume e-coupon as the first sample.

**a.** Compute the test statistic. **(Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)**

Test Statistics.............

**b.** Compute the *p*-value. NOTE: P-value calculators are available through online search. **(Round your answer to 4 decimal places.)**

P-value...............