Question

Periodically a bottling company gets complaints that their bottles are not holding enough liquid. To test this claim the bottling company randomly samples 70 bottles and finds the average amount of liquid held by the bottles is 9.896 ounces with a standard deviation of .46 ounce. Suppose the​ p-value of this test is .054. State the proper conclusion.

Answer 1

The null hypothesis was not rejected at 1% and 5% level of significance, but was rejected at 10% level of significance.

Explanation:

The complaints made by the customers of a bottling company is that their bottles are not holding enough liquid.

The company wants to test the claim.

Let the mean amount of liquid that the bottles are said to hold be, μ₀.

The hypothesis for this test can be defined as follows:

H₀: The mean amount of liquid that the bottles can hold is μ₀, i.e. μ = μ₀.

Hₐ: The mean amount of liquid that the bottles can hold is less than μ₀, i.e. μ < μ₀.

The p-value of the test is, p = 0.054.

Decision rule:

The null hypothesis will be rejected if the p-value of the test is less than the significance level. And vice-versa.

• Assume that the significance level of the test is, α = 0.01.

The p-value = 0.054 > α = 0.01.

The null hypothesis was failed to be rejected at 1% level of

significance. Concluding that the mean amount of liquid that the

bottles can hold is μ₀.

• Assume that the significance level of the test is, α = 0.05.

The p-value = 0.054 > α = 0.05.

The null hypothesis was failed to be rejected at 5% level of

significance. Concluding that the mean amount of liquid that the

bottles can hold is μ₀.

• Assume that the significance level of the test is, α = 0.10.

The p-value = 0.054 < α = 0.10.

The null hypothesis will be rejected at 10% level of

significance. Concluding that the mean amount of liquid that the

bottles can hold is less than μ₀.