Question

As Americans have become more environmentally conscious, there has been a social shift in general public’s feelings towards recycling. In recent years, a number of companies have gone into the business of collecting used newspapers from households and recycling them. A financial analyst for one such company has recently determined that the firm would make a profit if the mean weekly newspaper collection from households exceeded 2 pounds.The test statistic is found to be t = 2.480. Match the probabilities (p-values) below to the claim which would be tested to determine if the firm would be profitable. PLEASE EXPLAIN YOUR WORK.

0.9923

0.0154

0.0077

(a) greater than alternative

(b) not-equal-to alternative

(c) less than alternative

Answer 1

Given our test statistic t=2.480 . If we look at t-tables we see that t_26,.01 = 2.479. Hence our  ?=.01.

We reject the null hypothesis if our p-value < ? . Hence we select our alternative hypothesis accordingly.

1) p-value = .9924 . Since p-value > ? , we fail to reject null hypothesis. Hence our null hypothesis should contain the profit condition , i.e

H₀ :  ? = > 2 v/s

H_a : ? < 2 . Hence less than alternative.

3) p-value = 0.0077 . Since p-value <   ? , we have sufficient evidence to reject null hypothesis. Hence our alternative hypothesis should contain the profit condition , i.e

H₀ :  ? = < 2 v/s

H_a : ? > 2 . Hence greater than alternative.

2) p-value = 0.0154 , p/2 = 0.0077 . In this case also we would fail to reject the null hypothesis. If we would use a not-equal to alternative , we have a two sided tail, with ?=0.05 on both sides . Hence we would fail to reject H₀ . If the firm would make a profit from exactly 2 pounds, then not-equal-to alternative should be used. i.e.

H₀ :  ? = 2 v/s

H_a : ??2 . Hence not equal to alternative.

If greater than 2 is required, then case 1 is applicable.