Question

question 2 of 6, step 3 of 3
3/20
correct

5	93	70	18	115	107
6	144	142	19	78	57
7	127	141	20	140	145
8	60	64	21	69	58
9	149	146	22	150	126
10	93	105	23	148	158
11	109	105	24	86	70
12	148	123	25	65	66
13	93	106

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step 3 of 3: make the decision and state the conclusion in terms of the original question.
answer
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• we fail to reject the null hypothesis and conclude that there is sufficient evidence at an ( alpha = 0.05 ) level of significance to say it is less expensive to purchase textbooks from the online retailers than from local bookstores.
• we reject the null hypothesis and conclude that there is sufficient evidence at an ( alpha = 0.05 ) level of significance to say it is less expensive to purchase textbooks from the online retailers than from local bookstores.
• we reject the null hypothesis and conclude that there is insufficient evidence at an ( alpha = 0.05 ) level of significance to say it is less expensive to purchase textbooks from the online retailers than from local bookstores

Explanation:

To determine the correct option, we analyze the logic of hypothesis testing. When we reject the null hypothesis, it means there is sufficient evidence (at the given significance level, here \(\alpha = 0.05\)) to support the alternative hypothesis. The alternative hypothesis in this context is that it is less expensive to purchase textbooks from online retailers than local bookstores. So if we reject the null, we conclude there is sufficient evidence for the alternative. The second option states "We reject the null hypothesis and conclude that there is sufficient evidence at an \(\alpha = 0.05\) level of significance to say it is less expensive to purchase textbooks from the online retailers than from local bookstores," which follows the hypothesis - testing conclusion logic. The first option says we fail to reject (which would mean not enough evidence), and the third option has a contradiction (rejecting but saying insufficient evidence).

Answer:

We reject the null hypothesis and conclude that there is sufficient evidence at an \(\alpha = 0.05\) level of significance to say it is less expensive to purchase textbooks from the online retailers than from local bookstores.