Question

In: Statistics and Probability

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...

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 36 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 (Click to select)=≠ 16 versus Ha : μ (Click to select)≠= 16

(b) Suppose that Crown Bottling Company decides to use a level of significance of α = 0.01, and suppose a random sample of 36 bottle fills is obtained from a test run of the filler. For each of the following four sample means— x¯x¯ = 16.06, x¯x¯ = 15.96, x¯x¯ = 16.03, and x¯x¯ = 15.90 — 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¯ = 16.06

z
p-value

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

x¯x¯⁢ = 15.96

z
p-value


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


x¯x¯⁢ = 16.03

z
p-value


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


x¯x¯⁢ = 15.90

z
p-value


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

Solutions

Expert Solution


Related Solutions

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
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...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
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...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
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...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
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...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
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...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
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...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
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...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
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...
The Local Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
The Local Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Paradise 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...
1. The Crown Bottling Company has installed a new bottling process that will fill 12- ounce...
1. The Crown Bottling Company has installed a new bottling process that will fill 12- ounce bottles of Cola. Both overfilling and underfilling of bottles is undesirable. The company wishes to see whether the mean bottle fill, µ, is approximately the target of 12 ounces. The standard deviation of the process is such that σ=0.41. The company samples 32 bottles. Use a hypothesis test, at a 5% level of significance, and the sample mean to determine whether the filler should...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT