Question

Please use the traditional approach and state which table you use to find your crititcal values.

#6 A machine that bottles 12 oz soft-drinks is being tested. The manufacturer wants to ensure that the machine puts at least 12 oz into each bottle on the average. A random sample of 24 bottles produces an average volume of 12.07 oz with a standard deviation of 0.11 oz. Assuming that volume is normally distributed, test the manufacturer's hypothesis at the 0.05 level of significance.

A tire company believes that their new line of tires can increase gas mileage by at least 2 mpg over mileage achieved by using a competitor's tire. Twelve cars were run for 1000 miles on the competitor's tires and 1000 miles on the new tires. Assume that the difference between tire mileages are normally distributed.

a) Can the tire manufacturer support his claim at the 0.10 level of significance?

b) Can the manufacturer state that the tires improved gas mileage

Answer 1

NULL HYPOTHESIS H0:

ALTEWRNATIVE HYPOTHESIS Ha: (One tailed test)

n=24 , xbar= 12.07 Oz and s= 0.11 Oz alpha= 0.05

Under null hypothesis H0 test statistics is

Degrees of freedom= n-1= 24-1= 23

Critical value of t with 23 d.f for one tailed test at 0.05level of significance is 1.714

By using t table.

DECISION: REJECT H0 : IF Critical value of t <Calculated value of t

CONCLUSION: Since critical value of t is smaller than calculated value of t we therefore reject H0 and conclude that we have sufficientevidence to show that the machine puts at least 12 oz into each bottle on the average.

NOTE: In second part few things are missing .Like standard deviation and means.