Question

The quality control department of a shampoo manufacturer requires the mean weight of bottles of its product to be 12 fluid ounces. A sample of 20 consecutive bottles filed by the same machine is taken from the assembly line and measured. The results (in fluid ounces) were as follows:

12.9   12.5     12.2 12.3 11.5 11.8   11.7   12.2 12.4 12.6 12.5 12.8 11.8 11.5 11.6 12.7 12.6 12.7 12.8 12.2

Do these data provide sufficient evidence to indicate a lack of randomness in the pattern of overfitting and underfitting? Use α=0.05.

Answer 1

Solution :

x	x2
12.9	166.41
12.5	156.25
12.2	148.84
12.3	151.29
11.5	132.25
11.8	139.24
11.7	136.89
12.2	148.84
12.4	153.76
12.6	158.76
12.5	156.25
12.8	163.84
11.8	139.24
11.5	132.25
11.6	134.56
12.7	161.29
12.6	158.76
12.7	161.29
12.8	163.84
12.2	148.84
∑x=245.3	∑x2=3012.69

Mean ˉx=∑xn

=12.9+12.5+12.2+12.3+11.5+11.8+11.7+12.2+12.4+12.6+12.5+12.8+11.8+11.5+11.6+12.7+12.6+12.7+12.8+12.2/20

=245.3/20

=12.265

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

=√3012.69-(245.3)220/19

=√3012.69-3008.6045/19

=√4.0855/19

=√0.215

=0.4637

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 12

Ha :     12

Test statistic = t

= ( - ) / S / n

= (12.26-12) / 0.46 / 20

= 2.528

Test statistic = t =  2.528

P-value =0.0205

= 0.05  

P-value <

0.0205 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that