Question

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample of 31 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 16 ounces, then the filler’s initial setup will be readjusted.

(a) The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test.

H₀ : μ =  Correct16 versus H_a : μ ≠  Correct16

(b) Suppose that Crown Bottling Company decides to use a level of significance of α = 0.01, and suppose a random sample of 31 bottle fills is obtained from a test run of the filler. For each of the following four sample means— x⎯⎯x¯ = 16.05, x⎯⎯x¯ = 15.95, x⎯⎯x¯ = 16.07, and x⎯⎯x¯ = 15.93 — determine whether the filler’s initial setup should be readjusted. In each case, use a critical value, a p-value, and a confidence interval. Assume that σ equals .1. (Round your z to 2 decimal places and p-value to 4 decimal places and CI to 3 decimal places.)

x⎯⎯x¯ = 16.05

z	.31 .31 Incorrect
p-value	.7580 .7580 Incorrect

CI            [   Not attempted,  Not attempted]      

x⎯⎯x¯⁢ = 15.95

z	Not attempted
p-value	Not attempted

CI              [   Not attempted,  Not attempted]   

x⎯⎯x¯⁢ = 16.07

z	Not attempted
p-value	Not attempted

CI                  [   Not attempted,  Not attempted]     

x⎯⎯x¯⁢ = 15.93

z	Not attempted
p-value	Not attempted

CI              [   Not attempted,  Not attempted]    

Answer 1

b)for xbar =16.05

test stat z = '(x̄-μ)*√n/σ=	2.78
p value        =	0.0054

CI =16.004 , 16.096

for xbar =15.95

test stat z = '(x̄-μ)*√n/σ=	-2.78
p value        =	0.0054

CI =15.904 , 15.996

for xbar =16.07

test stat z = '(x̄-μ)*√n/σ=	3.90
p value        =	0.0001

CI =16.024 , 16.116

for xbar =15.93

test stat z = '(x̄-μ)*√n/σ=	-3.90
p value        =	0.0001

  CI =15.884 , 15.976