Question

In: Statistics and Probability

1. To estimate the mean triglyceride levels of people in West Palm Beach, a blood test...

1. To estimate the mean triglyceride levels of people in West Palm Beach, a blood test on 30 randomly selected people was conducted and yielded a mean triglyceride level of 220, with a standard deviation of 12. Construct a 95% confidence interval for the true average triglyceride level of people in West Palm Beach. Round your answer to three decimal places.

a. (218.868, 229.132)
b. (215.519, 224.481)
c. (214.967, 233.033)
d. (219.741, 230.259)

Expert Solution

solution

Given that,

= 220

s =12

n = 30

Degrees of freedom = df = n - 1 = 30- 1 = 29

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,29= 2.045 ( using student t table)

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.045 * (12 / $\sqrt$ 30) = 4.480

The 95% confidence interval estimate of the population mean is,

- E < < + E

220 - 4.480 < < 220+ 4.480

215.519 < < 224.481

( 215.519,224.481)

orchestra answered 1 year ago

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