Question

In a 4-week study about the effectiveness of using magnetic insoles to treat plantar heel pain, 52 subjects wore magnetic insoles and 41 subjects wore nonmagnetic insoles. The results are shown at the right. At a =0.06, can you support the claim that there is a difference in the proportion of subjects who feel better between the two groups? Assume the random samples are independent. Complete parts (a) through (e). Do you Feel Better? Magnetic Insoles Yes 14 No 38 Nonmagnetic Insoles Yes 16 No 25 (a) Identify the claim and state Ho and H, The claim is "the proportion of subjects who feel better with magnetic Insoles is different than those who feel better with nonmagnetic insoles." Let P, represent the population proportion for the magnetic insoles and P2 represent the population proportions for the nonmagnetic insoles. State Ho and H. Click to select your answer(s).

Answer 1

Answer Date: 31/07/2020 a) To test the claim is that the proportion of subjects who feel better with magnetic insoles is different than those who feel better with nonmagnetic insoles. The null and alternative hypothesis is, H: P. = P2 H.: P. P2 b) The Z-critical value is, From the standard normal table, the z-critical value for two-tailed at 94% confidence is 1.88. The Z-critical value is -1.88, 1.88

The rejection region is, Reject the null hypothesis, if the z-test statistics is less than the z-critical value which is - 1.88. Reject the null hypothesis, if the Z-test statistics is higher than the z-critical value which is 1.88. The correct option is D The z-test statistics is, First, compute pooled proportion then find the z-test statistics. The pooled proportion is, p = x₂ + x₂ M + h 14 +16 52 +41 = 0.3226 =

The z-test statistics is, Pi - P2 Z= 1 1 p(1 - p) + n n2 14/52 - 16/41 1 1 0.3226(1 -0.3226) X + 52 41 = -1.24 The Z-test statistics is -1.24 d) Decision The z-test statistics is -1.24 is not falls in the critical region which is -1.88, so fail to reject the null hypothesis is rejected at 6% level of significance. The correct option is 2

e) Conclusion There is insufficient evidence to support the claim that there is a difference in proportion of subjects who feel better between the two groups. The result is not statistically significant. The correct option is B