Answer:
The null hypothesis was not rejected at 1% and 5% level of significance, but was rejected at 10% level of significance.
Step-by-step 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, <em>μ₀</em>.
The hypothesis for this test can be defined as follows:
<em>H₀</em>: The mean amount of liquid that the bottles can hold is <em>μ₀,</em> i.e. <em>μ</em> = <em>μ₀</em>.
<em>Hₐ</em>: The mean amount of liquid that the bottles can hold is less than <em>μ₀,</em> i.e. <em>μ</em> < <em>μ₀</em>.
The <em>p</em>-value of the test is, <em>p</em> = 0.054.
Decision rule:
The null hypothesis will be rejected if the <em>p</em>-value of the test is less than the significance level. And vice-versa.
- Assume that the significance level of the test is, <em>α</em> = 0.01.
The <em>p</em>-value = 0.054 > <em>α</em> = 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 <em>μ₀</em>.
- Assume that the significance level of the test is, <em>α</em> = 0.05.
The <em>p</em>-value = 0.054 > <em>α</em> = 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 <em>μ₀</em>.
- Assume that the significance level of the test is, <em>α</em> = 0.10.
The <em>p</em>-value = 0.054 < <em>α</em> = 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 <em>μ₀</em>.
