Question

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random sample of 49 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces with a standard deviation of 0.35 ounces.

A) Specify the rejection region for  = 0.01. Reject H0 if

B) What is the conclusion

Answer 1

Solution :

= 12

=11.88

S =0.35

n = 49

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 12

Ha :     12

Test statistic = t

= ( - ) / S / n

= (11.88-12) / 0.35 / 49

= −2.4

Test statistic = t =−2.4  

P-value =0.0203

= 0.01

P-value >

0.0203 > 0.01

Fail to reject the null hypothesis .

There is not sufficient evidence to claim that the population mean μ is different than 12, at the 0.01 significance level.