contestada

A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sample of 22 bags from line 1 and a random sample of 25 bags from line 2 were recently selected. Each bag’s weight was measured and the following summary measures from the samples are reported:

Production Line 1

Sample size 22

Sample mean weight (lbs.) 24.89

Sample variance 0.0081

Production Line 2

Sample size25

Sample mean weight (lbs.) 25.03

Sample variance 0.0196

Construct a 96% confidence interval estimate of the average difference in fill weights for the 2 production lines. Interpret the practical meaning of the resulting confidence interval, in the context of the problem, in plain English.

Respuesta :

danialamin

Answer:

The confidence interval is (-0.70, 0.98).this indicates that with 96% confidence, it can be defined that the value of sample of difference will be between this interval.

Explanation:

The given data is as follows:

μ1 =24.89

n1=22

[tex]\sigma_1^2 =0.0081[/tex]

μ2=25.03

n2=25

[tex]\sigma_2^2 =0.0196[/tex]

With this data the mean difference is given as

CI @ 96% is given as

[tex](x_1,x_2)=(\mu_2-\mu_1) \mp z_{\alpha}\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}[/tex]

The values are as given above. [tex]z_{\alpha}[/tex] is 2.05 for the confidence interval 96%.

[tex](x_1,x_2)=(\mu_2-\mu_1) \mp z_{\alpha}\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\\(x_1,x_2)=(25.03-24.89) \mp 2.05\sqrt{\frac{0.0081}{22}+\frac{0.0196}{25}}\\(x_1,x_2)=(0.14) \mp 0.84\\(x_1,x_2)=(-0.70, 0.98)[/tex]

So The confidence interval is (-0.70, 0.98).this indicates that with 96% confidence, it can be defined that the value of sample of difference will be between this interval.

Otras preguntas