You are advised to perform the appropriate hypothesis test using pencil and paper, along with a calculator and statistical tables, and then use your working to answer the questions below.

A filling operation for spice bottles has a historical standard deviation of7 grams. When in perfect adjustment, the mean filling weight is 53 grams. A quality control inspector periodically selects at random 36 spice bottles and uses the sample mean filling weight to determine whether there is strong evidence that the process is not in perfect adjustment.From one inspection, she finds that the mean filling weight of the 36 bottles is 49.2 grams.

Use this sample statistic to determine whether there is sufficient evidence at the 1% level of significance to assert that the process is not in perfect adjustment.

(a) According to the null hypothesis, the value of the population mean isAnswer

grams. (Answer in the form xx.x)

(b) Is the test one-tailed or two-tailed? Answer:Answer

(answer 1 or 2)

(c) To 3 decimal places the upper tail critical value of the test statistic for this hypothesis test is:Answer

(Answer in the form x.xxx)

(d) To 3 decimal places the test statistic calculated from the sample is:Answer

(Answer in the formx.xxx or -x.xxx)

(e) Is the null hypothesis rejected at the 1% level? Answer:Answer

(Answer YES or NO)

(f) Does this mean that filling process is in perfect adjustment?Answer:Answer

(Answer YES or NO)

(g) Is it necessary to assume the fill amounts are normally distributed in order to perform this test?Answer

(Answer YES or NO)