Question

1. You work for the FTC.  A manufacturer of detergent claims that the mean weight of detergent is 4.25 lb.  You take a random sample of 64 containers.  You calculate the sample average to be 4.238 lb. with a standard deviation of .127 lb.  At the .05 level of significance, is the manufacturer correct?

2. Is the average capacity of batteries less than 120 ampere-hours?  A random sample of 49 batteries had a mean of 118.47 and a standard deviation of 3.66.  Assume a normal distribution. Test at the 0.1 level of significance.

3. A random sample of graduated students from Acsenda is taken to identify how much of students find a job after their graduation. 348 out of 400 students had a satisfying job. The management has concluded that 90% of graduate students have found a satisfying job. Test the hypothesis at 0.05 level of significance to see if the management is correct.

Answer 1

1.

The null and alternative hypothesis is ,

The test is two-tailed test.

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=64-1=63

The critical values are ,

Rejection rule : Reject Ho , if t-stat>1.998 and t-stat<-1.998

The test statistic is ,

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

Conclusion : Hence , there is sufficient evidence to support the manufacturer's claim.