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Chapter 8: Problem 59

A magazine advertisement claims that wearing a magnetized bracelet will reduce arthritis pain in those who suffer from arthritis. A medical researcher tests this claim with 233 arthritis sufferers randomly assigned either to wear a magnetized bracelet or to wear a placebo bracelet. The researcher records the proportion of each group who report relief from arthritis pain after 6 weeks. After analyzing the data, he fails to reject the null hypothesis. Which of the following are valid interpretations of his findings? There may be more than one correct answer. a. The magnetized bracelets are not effective at reducing arthritis pain. b. There's insufficient evidence that the magnetized bracelets are effective at reducing arthritis pain. c. The magnetized bracelets had exactly the same effect as the placebo in reducing arthritis pain. d. There were no statistically significant differences between the magnetized bracelets and the placebos in reducing arthritis pain.

Short Answer

Expert verified
Based on the context of the question, the correct interpretations would be Option B and Option D.

Step by step solution

01

Understand the Scenario and Hypothesis Testing

First, understand the background of this scenario with respect to hypothesis testing. In hypothesis testing, researchers make an initial assumption, termed the null hypothesis, then collect and analyze data to determine if evidence exists to reject this null hypothesis in favor of an alternative hypothesis. In this scenario, the null hypothesis was probably that the magnetized bracelets had no effect on arthritis pain compared to a placebo.
02

Interpret Option A

Option A states: 'The magnetized bracelets are not effective at reducing arthritis pain.' Technically this cannot be inferred because failure to reject the null hypothesis does not mean that null hypothesis (i.e., no difference between the effects of the magnetized bracelet and the placebo) is true. It merely means that the collected data doesn鈥檛 provide strong enough evidence to reject the null hypothesis. There is a possibility that with more data or different samples, the inference might be different.
03

Interpret Option B

Option B states: 'There's insufficient evidence that the magnetized bracelets are effective at reducing arthritis pain.' This is a valid interpretation. Since the null hypothesis was not rejected, it suggests that there isn't enough evidence to conclude that the magnetized bracelets have a significant effect on reducing arthritis pain.
04

Interpret Option C

Option C states: 'The magnetized bracelets had exactly the same effect as the placebo in reducing arthritis pain.' This statement is misleading. Even though the null hypothesis wasn't rejected, it doesn't mean that the magnetized bracelets and the placebo had 'exact' same effect. It only means that there is insufficient evidence to conclude that there is a significant difference between the two.
05

Interpret Option D

Option D says: 'There were no statistically significant differences between the magnetized bracelets and the placebos in reducing arthritis pain.' This is a valid interpretation. In the context of hypothesis testing, failure to reject the null hypothesis generally means that there were no statistically significant differences detected.

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