Question

# A filling machine, when in proper adjustment, fills the bottles with 32 ounces of liquid. A...

A filling machine, when in proper adjustment, fills the bottles with 32 ounces of liquid. A random sample of 19 bottles is selected, and the contents are measured. The sample mean was 31.7 ounces, with a sample standard deviation of 0.55 ounces. With a 0.05 level of significance, test to see if the machine is in proper adjustment. Assume the distribution of the population is normal.

The null and alternative hypothesis is ,

The test is two-tailed test.

Since , the population standard deviation is not known.

Therefore , use t-test.

The test statistic is ,

Now , df=degrees of freedom=n-1=19-1=18

The critical values are ,

Rejection Rule : Reject Ho , If t-stat<-2.101 or t-stat>2.101

Decision : Here , t-stat=-2.38<-2.101

Therefore , reject Ho.

Conclusion : There is not sufficient evidence to conclude that the machine is in proper adjustment..

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