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kornut5536
14.04.2020 •
Mathematics
A large university is interested in the outcome of a course standardization process. They have taken a random sample of 100 student grades, across all instructors. The grades represent the proportion of problems answered correctly on a midterm exam. The sample proportion correct was calculated as 0.78. a. Construct a 90% confidence interval on the population proportion of correctly answered problems. b. Construct a 95% confidence interval on the population proportion of correctly answered problems.
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Ответ:
Step-by-step explanation:
a)
Number of sample, n = 100
p = 0.78
q = 1 - p = 1 - 0.78
q = 0.22
For a confidence level of 90%, the corresponding z value is 1.645.
The formula for determining the error bound for the proportion is
z × √pq/n
= 1.645 ×√(0.78 × 0.22)/100
= 1.645 × 0.0414 = 0.068
The upper boundary of the population proportion is
0.78 + 0.068 = 0.85
The lower boundary of the population proportion is
0.78 - 0.068 = 0.71
b) For a confidence level of 95%, the corresponding z value is 1.96.
Therefore,
= 1.96 ×√(0.78 × 0.22)/100
= 1.96 × 0.0414 = 0.081
The upper boundary of the population proportion is
0.78 + 0.081 = 0.86
The lower boundary of the population proportion is
0.78 - 0.081 = 0.7
Ответ:
#3 1,177.50^3mm
Step-by-step explanation: