Question

Baby weight: Following are weights, in pounds, of 10 two-month-old baby girls. It is reasonable to assume that the population is approximately normal.

12.66 8.63 11.87 14.13 12.32 9.34 10.30 12.34 12.23 11.48

Construct a 90% interval for the mean weight of two-month-old baby girls. Round the answers to three decimal places.

____< u <_____

Answer 1

Solution:

x	x2
12.66	160.2756
8.63	74.4769
11.87	140.8969
14.13	199.6569
12.32	151.7824
9.34	87.2356
10.3	106.09
12.34	152.2756
12.23	149.5729
11.48	131.7904
∑x=115.3	∑x2=1354.0532

Mean ˉx=∑xn

=12.66+8.63+11.87+14.13+12.32+9.34+10.3+12.34+12.23+11.48 / 10

=115.3/10

=11.53

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

=√1354.0532-(115.3)210/9

=√1354.0532-1329.409/9

=√24.6442/9

=√2.7382

=1.6548

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t /2,df = t0.05,9 =1.833

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

=1.833 * (1.65 / 10)

= 0.96

Margin of error = 0.96

The 90% confidence interval estimate of the population mean is,

- E < < + E

11.53 - 0.96 < < 11.53 + 0.96

10.57 < < 3.70

(10.57, 12.49 )