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A drug manufacturer wants to estimate the mean heart rate for…

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A drug manufacturer wants to...
A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart condition. Because the condition is rare, the manufacturer can only find 15 people with the condition currently untreated. From this small sample, the mean heart rate is 92 beats per minute with a standard deviation of 8.
(a) Find a 98% confidence interval for the true mean heart rate of all people with this untreated condition. Show your calculations and/or explain the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it
Submitted: 8 years ago.Category: Math Homework
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Answered in 12 minutes by:
6/17/2010
Math Tutor or Teacher: rajeevanpillai, Master's Degree replied 8 years ago
rajeevanpillai
rajeevanpillai, Master's Degree
Category: Math Homework
Satisfied Customers: 741
Experience: M.Sc Statistics MPhil Statistics
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n = 15
xbar = 92
s = 8
degrees of freedom = n-1 = 15-1 = 14
1-α = 98% = 0.98
α = 1-0.98 = 0.02
α/2 = 0.02/2 = 0.01
t(0.01,14) = 0.6245

t(0.01,14) * s/sqrt(n) = 2.6245 * 8 / sqrt(15) = 5.4211

The 98% confidence limits are
xbar ± t(0.01,14) * s/sqrt(n) = 92 ± 5.4211 = 86.5789, 97.4211

The 98% confidence interval for the population mean μ is (86.579, 97.421)


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