please provide detailed explanation for each part of the question.
We are interested in estimating the mean systolic blood pressure for female diabetics between the ages of 30 and 34. For the purposes of this question you may assume that blood pressure in this population has a normal distribution.
a. A random sample of 10 women is selected from this population. The average systolic blood pressure in this sample is 130 mmHg. The sample standard deviation is 9.2 mmHg. Calculate a 95% confidence interval for , the mean systolic blood pressure in the population of female diabetics aged 30 to 34.
b. Provide a formal interpretation of your confidence interval in a) in words. (What does “95% confidence” mean?)
c. Can you determine how large the random sample of women would need to be for a 99% confidence interval to have a total width of 10 mmHg? If so, provide the sample size. If not, explain why.
a) Confidence interval, CI = Z*
n = 10
= 130 mmHg
s = 9.2 mmHg
For 95% confidence level, Z* = 1.96
CI = 130 1.96 x
= 130 5.70
= (124.30, 135.70)
b) We are 95% confident that the mean systolic blood pressure for female diabetics between the ages of 30 and 34 will be within the interval (124.30, 135.70)
c) If the total width of confidence interval = 10,
Margin of error, E = 10/2 = 5
E = Z*
For 99% CI, Z* = 2.576
5 = 2.576 x
n = 24
For a 99% confidence interval to have a total width of 10 mmHg, the sample size required is 24.
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