Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variations from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91. Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. b. Calculate the test statistic. c. Find the P-value. d. What is the conclusion?

A

a. H0: the mean volume of all the bottles is 6 ounces. Ha: the mean volume of all the bottles is not equal to 6 ounces.

b. The z-score is equal to:

z = ((x-μ)/√(σ2/N)) = 5.989-(6/√(0.09/10)) = -0.115

c. The p-value is equal to 0.907.
d. The null hypothesis should be accepted.

Answer by Academic.tip's expert
An answer to this question is provided by one of our experts who specializes in mathematics. Let us know how much you liked it and give it a rating.

Cite this page

Select a citation style:

References

Academic.Tips. (2021) 'Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variations from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91. Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. b. Calculate the test statistic. c. Find the P-value. d. What is the conclusion'. 15 July.

Reference

Academic.Tips. (2021, July 15). Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variations from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91. Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. b. Calculate the test statistic. c. Find the P-value. d. What is the conclusion? Retrieved from https://academic.tips/question/cough-a-lot-childrens-cough-syrup-is-supposed-to-contain-6-ounces-of-medicine-per-bottle-however-since-the-filling-machine-is-not-always-precise-there-can-be-variations-from-bottle-to-bott/

References

Academic.Tips. 2021. "Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variations from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91. Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. b. Calculate the test statistic. c. Find the P-value. d. What is the conclusion?" July 15, 2021. https://academic.tips/question/cough-a-lot-childrens-cough-syrup-is-supposed-to-contain-6-ounces-of-medicine-per-bottle-however-since-the-filling-machine-is-not-always-precise-there-can-be-variations-from-bottle-to-bott/.

1. Academic.Tips. "Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variations from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91. Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. b. Calculate the test statistic. c. Find the P-value. d. What is the conclusion?" July 15, 2021. https://academic.tips/question/cough-a-lot-childrens-cough-syrup-is-supposed-to-contain-6-ounces-of-medicine-per-bottle-however-since-the-filling-machine-is-not-always-precise-there-can-be-variations-from-bottle-to-bott/.


Bibliography


Academic.Tips. "Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variations from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91. Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. b. Calculate the test statistic. c. Find the P-value. d. What is the conclusion?" July 15, 2021. https://academic.tips/question/cough-a-lot-childrens-cough-syrup-is-supposed-to-contain-6-ounces-of-medicine-per-bottle-however-since-the-filling-machine-is-not-always-precise-there-can-be-variations-from-bottle-to-bott/.

Work Cited

"Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variations from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91. Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. b. Calculate the test statistic. c. Find the P-value. d. What is the conclusion?" Academic.Tips, 15 July 2021, academic.tips/question/cough-a-lot-childrens-cough-syrup-is-supposed-to-contain-6-ounces-of-medicine-per-bottle-however-since-the-filling-machine-is-not-always-precise-there-can-be-variations-from-bottle-to-bott/.

Copy