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.