## Related questions with answers

Question

In Relief from Arthritis published by Thorsons Publishers, Ltd., John E. Croft claims that over 40% of those who suffer from osteoarthritis receive measurable relief from an ingredient produced by a particular species of mussel found ff the coast of New Zealand. To test this claim, the mussel extract is to be given to a group of 7 osteoarthritic patients. If 3 or more of the patients receive relief, we shall not reject the null hypothesis that p =0 .4; otherwise, we conclude that p < 0.4. (a) Evaluate $\alpha$ assuming that p = 0.4. (b) Evaluate $\beta$ for the alternative p = 0.3.

Solution

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1 of 6- To test the claim that more than 40% of the osteoarthritic patients found relief from a certain product, the product is given to a group of $\color{black}{7}$ osteoarthritic patients. So, the sample size is $\color{#c34632}{n=7}$.
- If $\text{\textcolor{#19804f}{3 or more}}$ of the patients receive relief, we shall $\text{\textcolor{#19804f}{ accept the null hypothesis $H_0$: $p = 0.4$}}$.
- If $\text{\textcolor{#c34632}{less than 3 }}$ of the patients receive relief, we shall $\text{\textcolor{black}{ reject the null hypothesis}}$ and $\text{\textcolor{#c34632}{ accept the alternative hypothesis $H_1$: $p<0.4$}}$.

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