Question

a.If n = 21, x¯ = 44, and s = 10, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places. =    < u <

b.Assume that a sample is used to estimate a population mean μ . Find the 80% confidence interval for a sample of size 1058 with a mean of 65.2 and a standard deviation of 10.1. Enter your answer as a tri-linear inequality accurate to 3 decimal places.=    < μ <

c. The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 63.1 for a sample of size 27 and standard deviation 13.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.= <μ<   

d. Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a sample of size 209 with 21% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
CI=

e. If n = 590 and X = 472, construct a 99% confidence interval for the population proportion, p. Give your answers to three decimals

Answer 1

a)
Sample size (n) = 21
Standard deviation (s) = 10
Confidence interval(in %) = 99

Since we know that

Required confidence interval =
Required confidence interval = (44.0-6.2083, 44.0+6.2083)
Required confidence interval = (37.7917, 50.2083)
b)
Sample size (n) = 1058
Standard deviation (s) = 10.1
Confidence interval(in %) = 80
z @ 80.0% = 1.282
Required confidence interval =
Required confidence interval = (65.2-0.3981, 65.2+0.3981)
Required confidence interval = (64.8019, 65.5981)
c)
Sample size (n) = 27
Standard deviation (s) = 13.5
Confidence interval(in %) = 99

Required confidence interval =
Required confidence interval = (63.1-7.2193, 63.1+7.2193)
Required confidence interval = (55.8807, 70.3193)
d) Sample proportion = 0.21
Sample size (n) = 209
Confidence interval(in %) = 98
z @ 98% = 2.33
Since we know that

Required confidence interval = (0.21-0.0657, 0.21+0.0657)
Required confidence interval = (0.1443, 0.2757)
e) Sample proportion = 0.8
Sample size (n) = 590
Confidence interval(in %) = 99
z @ 99% = 2.576
Since we know that

Required confidence interval = (0.8-0.0425, 0.8+0.0425)
Required confidence interval = (0.7575, 0.8425)
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