Question

In a clinical study, 4200 subjects were vaccinated with a flu vaccine manufactured by growing cells in fertilized chicken eggs. Over a period of roughly 28 weeks, 32 of these subjects developed the flu. a. Find the observed statistic. Use the proper notation (7 or ). [2pts) b. Verify that the sample size is large enough to use the normal distribution to construct a confidence interval for the proportion of the population that were vaccinated with the vaccine but still developed the flu. [2 pts] C. Construct a 95% confidence interval for the proportion of the population that were vaccinated with the vaccine but still developed the flu. [5pts] d. Provide an interpretation of your interval in the context of the data. [2pts] e. According to your confidence interval in c), is it reasonable to assume that fewer than 1% of all people vaccinated will develop the flu? Clearly answer"yes "no" __. And provide an explanation for your answer. [2pts]

Answer 1

Given that Sample size n = 4200 x = 32 a) Now we have to find the sample proportion o. 32 sample proportion p -0.0076 4200 :: P = 0.0076. b) If sample size (n) > 30, we can use normal distribution to construct the confidence interval. In our problem, sample size = n = 4200 > 30 .. we can use normal distribution to construct the confidence interval.

c) Now we have to construct the 95% confidence interval for the population proportion(p).

Step (1): 95 1- 1-0.95 = 0.05 100 0.05 = 0.025 2 Step (2): 1 -0.025 = 0.975 Find the value of Za/2 such that P(Z < Za/2) = 0.975 From standard normal table Za/2 1.96 (Or) Use excel formula: ENORM.S.INV(0.975) Step (3): First find the margin of error MOE. 32 32 1 MOE = Za/2 p(1-0) n 4200 1.96 * 4200) = 0.003 4200 Step (4): 32 Lower bound= p – MOE 0.003 = 0.005 4200 Upper bound = P + MOE 32 + 0.003 = 0.011 4200

(0.005, 0.011).

d) Now we have to write the interpretation. Interpretation: One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

e) No, is the answer. Reason: Our 95% confidence interval is from 0.005 to 0.011. Our 95% confidence interval includes above 1% (0.01) also. It is not reasonable to assume that fewer than 1% of all people vaccinated will develop the flu. No, is the answer.

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