Question

In: Statistics and Probability

Listed below are weights(hectograms) of randomly selected girls at birth. Here are the summary statistics: n=12, =...

Listed below are weights(hectograms) of randomly selected girls at birth. Here are the summary statistics: n=12, = 31.167hg, s= 3.157hg. Use the sample data to construct a 95% confidence interval for the mean birth weight of girls.

33, 28, 33, 37, 31, 32, 31, 28, 34, 28, 33, 26

Expert Solution

Solution:
Mean ˉx=∑xn

=33+28+33+37+31+32+31+28+34+28+33+26 / 12

=374/12

=31.1667

= 31.17

s = 3.157

n = 12

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,11 =2.201

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

= 2.201 * (3.157 / $\sqrt$ 12)

= 2.006

Margin of error =2.006

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

- E < < + E

31.17 - 2.006 < < 31.17 + 2.006

29.164 < < 33.176

(29.164, 33.176 )

orchestra answered 1 year ago

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