Practice questions - Quiz 3 (2023)

c) 95% CI: -14 േ 1.96 ∙ 0.9491 7) In the sample of 88 individuals that are diagnosed with the flu, let 0.42 represent the proportion of individuals that have pneumonia. In the sample of 102 individuals that are not diagnosed with the flu, let 0.24 represent the proportion of individuals that have pneumonia. a) What is the standard error of the difference in the means of these two samples? b) What is the t-statistic for the hypothesis there is no difference between the population proportions of individuals presenting with pneumonia among those with the flu and among those without the flu? c) What is the 90% confidence interval for the difference in the proportion of individuals in the population? Answer: This is just a special case (Bernoulli) of problem 6 above. For the Bernoulli sample, we can figure out the sample standard deviation from the sample proportions… a) 𝑆𝐸ሺ𝑌 ത ி െ 𝑌 ത ேி ሻ ൌ ට ௦ ಷ మ ௡ ಷ ൅ ௦ ಿಷ మ ௡ ಿಷ ൌ ට ଴ . ସଶሺଵି଴ . ସଶሻ ଼଼ ൅ ଴ . ଶସሺଵି଴ . ଶସሻ ଵ଴ଶ ൌ 0.0675 b) 𝑡 ൌ ሺ଴ . ସଶି଴ . ଶସሻି଴ ଴ . ଴଺଻ହ c) 90% CI: 0.18 േ 1.64 ∙ 0.0675 11. Investing in two assets with a correlation coefficient of 0.7 will reduce which kind of risk? A) Market risk B) Firm ‐ specific risk C) Systematic risk D) None of the above Answer: B