Question

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Carpal tunnel syndrome (a painful wrist condition) can be treated with surgery or with a less-invasive wrist splint. A study of 176 patients was performed in 2002. Among the 88 patients that had surgery, 80% showed improvement after three months, but only 48% of those 88 patients who used the wrist splints showed improvement.

a. To construct a confidence interval for the difference in the proportions, what conditions must be checked?

b. Construct a 95% confidence interval for this difference.

c. ​​​​​​​Write a meaningful conclusion.

Answer 1

Cin The must we are 2002 all each other, independent ca) The conditions are: samples selected be randon In ithis case, selecting the entire sample in the year Since are taking values of one sample, we cannot if is that, randon an say sample But the as random selected hospital is randoms, (h) The samples are independenti IS based since, the improvement each people we ean consider this 1 sample, il selected regia donot which on depend on conditio is met 1o exist atleast There successes (110 and fullures, The condition in 10

already met based ito propter the information provided (b) Givco, Ni & 8 88 Nya P₂ 0:48 Pi 80 A Xz z NzP =) Xi = Nop ga xb, це 0.8888 42 2 toia calculated as, ca is The 95000 Picha2+ P2 (1-ô2) P + ze N2 e Iz 2 the Using 220.05, 11-420.45), 1.96 zez critical value 0 1880.2 +0:48*0.52 1.96 > OS 0.48 I ..CI 2 2 0.1869 0.454

the 95°l. for Therefore, difference between two the is population proportios 0.18 6 L. Pi-P2. 2 0.454 (c) confidcot, Ine are ar 9501. the true differrence that, betweon the population proportions is contained in the interval (0.186, 01454)
​​​​​Or since the 95 % CI doesnt contain the value zero, we can conclude the people who had done the surgery had a better chance to improvement than the ones who have done wrist splint.