Question

Listed below are weights (hectograms or hg) of randomly selected girls at birth. Use the sample data to construct a 95% confidence interval for the mean weight of girls.

33 28 33 37 31 32 31 28 43 28 33 26 30 31 28

Address the following questions:

What is alpha

What is Z_{α/2  or tα/2}

Which formula did you use and what is the Confidence Interval?

Answer 1

Solution:

x	x2
33	1089
28	784
33	1089
37	1369
31	961
32	1024
31	961
28	784
43	1849
28	784
33	1089
26	676
30	900
31	961
28	784
∑x=472	∑x2=15104

Mean ˉx=∑xn

=33+28+33+37+31+32+31+28+43+28+33+26+30+31+28/15

=472/15

=31.4667


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√15104-(472)215/14

=√15104-14852.2667/14

=√251.7333/14

=√17.981

=4.2404

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,14 =2.145

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

= 2.145 * (4.24 / 15)

= 2.35

Margin of error = 2.35

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

- E < < + E

31.47 - 2.35 < < 31.47+ 2.35

29.12 < < 33.82

(29.12, 33.82)