The Crown Bottling Company has just installed a new bottlingprocess that will fill 16-ounce bottles of the popular CrownClassic Cola soft drink. Both overfilling and underfilling bottlesare undesirable: Underfilling leads to customer complaints andoverfilling costs the company considerable money. In order toverify that the filler is set up correctly, the company wishes tosee whether the mean bottle fill, μ, is close to thetarget fill of 16 ounces. To this end, a random sample of 39 filledbottles is selected from the output of a test filler run. If thesample results cast a substantial amount of doubt on the hypothesisthat the mean bottle fill is the desired 16 ounces, then thefiller’s initial setup will be readjusted.
(a) The bottling company wants to set up ahypothesis test so that the filler will be readjusted if the nullhypothesis is rejected. Set up the null and alternative hypothesesfor this hypothesis test.

H₀ : μ (Click to select)≠= 16 versusH_a : μ (Click to select)=≠ 16

(b) Suppose that Crown Bottling Company decidesto use a level of significance of α = 0.01, and suppose arandom sample of 39 bottle fills is obtained from a test run of thefiller. For each of the following four sample means— x¯x¯ = 16.05,x¯x¯ = 15.95, x¯x¯ = 16.03, and x¯x¯ = 15.97 — determine whetherthe filler’s initial setup should be readjusted. In each case, usea critical value, a p-value, and a confidence interval.Assume that σ equals .1. (Round your z to 2 decimal placesand p-value to 4 decimal places and CI to 3 decimalplaces.)

x¯x¯ = 16.05

z
p-value

CI           [,]   (Click to select)Do not readjustReadjust

x¯x¯⁢ = 15.95

z
p-value

CI             [,]   (Click to select)Do not readjustReadjust

x¯x¯⁢ = 16.03

z
p-value

CI                 [,]   (Click to select)Do not readjustReadjust

x¯x¯⁢ = 15.97

z
p-value

CI             [,] (Click to select)ReadjustDo not readjust