Question

In: Statistics and Probability

In a random sample of 24 hip surgeries of a certain type, the mean surgery time...

In a random sample of 24 hip surgeries of a certain type, the mean surgery time was 136.9 minutes with a sample standard deviation of 22.6 minutes. Which of the following is a 99% confidence interval for the population mean surgery time?

a.

(127.36, 146.44)
b.

(123.95, 149.85)
c.

(128.99, 144.81)
d.

(125.02, 148.78)

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 136.9

sample standard deviation = s = 22.6

sample size = n = 24

Degrees of freedom = df = n - 1 = 24 - 1 = 23

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df  = t0.005,23 = 2.807

Margin of error = E = t/2,df * (s /n)

= 2.807 * ( 22.6 / 24)

Margin of error = E = 12.95

The 99% confidence interval estimate of the population mean is,

- E < < + E

136.9 - 12.95 < < 136.9 + 12.95

123.95 < < 149.85

( 123.95 , 149.85 )

Correct option :- a. ( 123.95 , 149.85 )

orchestra answered 2 years ago
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