A juice drink filling machine, when in perfect adjustment, fills ...

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A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. 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 .35 ounces.
 a. Formulate the hypotheses for a test to determine if the machine is in perfect adjustment.
  b. Compute the value of the test statistic.
  c. Compute the p-value and give your conclusion regarding the adjustment of the machine. Let  = .05.

Question 2

A university has 5,000 students. The manager of food services at the university is interested in determining the total lunch expenditure. A simple random sample of 121 lunch receipts was selected. The sample showed an average of 3 with a standard deviation of 0.40.
 a. Estimate the standard error of the sample mean.
  b. Develop an approximate 95 confidence interval for the population mean.
  c. Estimate the population's total expenditure for lunch.
  d. Develop an approximate 95 confidence interval for the total expenditure for lunch.

[Bsand8]

Answer to Question 1

a. H0:  = 12 ounces
Ha:   12 ounces
b. t = -2.4
c. p-value is between .02 and .05; therefore, reject H0; the machine needs to be adjusted.

Answer to Question 2

a. 0.0359
b. 2.93 to 3.07 (rounded)
c. 15,000
d. 14,640.79 to 15, 359.21