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In: Statistics and Probability

True or False: An epidemiologist is worried about the prevalence of the flu in East Vancouver...

True or False:

An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 336 people living in East Vancouver and finds that 38 have recently had the flu.

For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of East Vancouver residents who have recently had the flu.

A. 11.31% (38/336) of East Vancouver residents have recently had the flu.  ? true false

B. There is a 95% probability that the true proportion of East Vancouver residents who have recently had the flu equals 38/336.  ? true false

C. If another random sample of 336 East Vancouver residents is drawn, there is a 95% probability that the sample proportion of East Vancouver residents who have recently had the flu equals 38/336.  ? true false

D. If many random samples of 336 East Vancouver residents are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of East Vancouver residents who have recently had the flu.   ? true false

E. If many random samples of 336 East Vancouver residents are drawn, 95% of the resulting confidence intervals will contain the value 38/336.  ? true false

Solutions

Expert Solution

A. 11.31% (38/336) of East Vancouver residents have recently had the flu.

Answer: False

A sample of 336 people of East Vancouver residents have recently had the flu. Not the entire population.

B. There is a 95% probability that the true proportion of East Vancouver residents who have recently had the flu equals 38/336.

Answer: False

C. If another random sample of 336 East Vancouver residents is drawn, there is a 95% probability that the sample proportion of East Vancouver residents who have recently had the flu equals 38/336.

Answer: False

D. If many random samples of 336 East Vancouver residents are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of East Vancouver residents who have recently had the flu.

Answer: True

E. If many random samples of 336 East Vancouver residents are drawn, 95% of the resulting confidence intervals will contain the value 38/336.

Answer: False

orchestra answered 2 years ago
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