Please answer 3 q’s all related pecies y seconds Questions 1 through 3 refer to

Question

Please answer 3 q’s all related pecies y seconds Questions 1 through 3 refer to the following setup. In running a white cell count, a drop of blood is smeared thin stained with Wright's stain, and examined under a microscope. Set 20 Of 112 white cells counted, were neutrophils, a white cell produced in the bone marrow whose function e up infective agents in the blood. Let p denote the true proportion of neutrop the white cells in this individual. i, Compute the lower limit of an 82% confidence interval for p. 075? 1.3408-Jo. 75 (aas 6.GAS s there any evidence that the true proportion of neutrophils among the white cells in this individual is above 0.70? Compute the P-value for the appropriate test. 2. I 3. Use the results of the sample of size 112 as a pilot study to determine the sample size needed 4 percentage points with 90% confidence. to estimate p within 29

Explanation / Answer

a) Lower limit of 82% confidence level = p - z critical *sqrt(pq/n))

= 0.75 - 1.3408 * sqrt(0.75 * 0.25/112))

= 0.6951

b) First we compute z score of 0.7

Z score = p - P /sqrt(PQ/n)

= 0.75 - 0.7 / sqrt(0.7 * 0.3/112))

= 1.15

p value = p(Z > 1.15) = 0.1251

c) n = (Zc / E)2 PQ

= (1.645 / 0.04)2 0.75 * 0.25

= 317.11

Approximately 318

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