Question

1. (5 pts) A researcher wants to estimate, at 92% confidence level, the proportion of Covid-19 symptomatic patients that have diabetes. The researcher wants estimate to be within three percentage points from the true proportion. What is the sample size needed if we have no pre-estimate of the proportion?

2. (10 pts) A researcher took a sample of 1000 healthy people, all of whom say they do not have diabetes, and tested their blood sugar. It turns out that 23 people actually have diabetes. Using this sample, construct a 95% confidence interval of the proportion of people who actually have diabetes out of people who think they don’t have it. Don’t forget to Check the requirements (5 pts), as well as Compute the confidence interval (3pts)l and state the Conclusion in context (2 pts). Show work completely and clearly.

(Data from this problem are made up, but based on the CDC's National Diabetes Statistics Report)

Answer 1

Solution:

Given :

Confidence level = c = 92%

Margin of Error = E = 3% = 0.03

No pre-estimate of the proportion is given, thus we use p = 0.5

Formula :

Zc is z critical value for c = 0.92 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.92 ) / 2 = 1.92 /2 = 0.9600

Thus look in z table for Area = 0.9600 or its closest area and find corresponding z critical value.

Area 0.9599 is closest to 0.9600 and it corresponds to 1.7 and 0.05

Thus Zc = 1.75

thus

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