Question

How much juice? Refer to Exercises 3 and 11 .

a. What conclusion would you make at the $\alpha =0.10\alpha =0.10$level?

b. Would your conclusion from part (a) change if a 5 \% significance level was used instead? Explain your reasoning.

Short answer

Part (a)There is sufficient convincing evidence that the correct mean volume of liquid is different from $180$millilitres.

Part (b)Yes,There is enough convincing evidence that the true mean volume of liquid is different from $180$millilitres.

Step-by-step solution

Part (a) Step 1:Given information

$\alpha =0.10\alpha =0.10$

Part (b) Step 2:Explaination

$P=0.0589$

$\alpha =0.10$

$\text{Given claim is mean is}180$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

$H_0:\mu =180$

$H_1:\mu \ne 180$

If the $P$-value is smaller than the significance level $\alpha$, then reject the null hypothesis:

$0.0589<0.10\Rightarrow \text{Reject}{H}_0$

There is sufficient convincing evidence that the correct mean volume of liquid is different from $180$millilitres.

Part (b) Step 1:Given information

A$5\%$ significance level was used

Part (b) Step 2:Explaination

$P=0.0589$

$\alpha =0.10$

$\text{Given claim of mean is}180.$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

$H_0:\mu =180$

$H_1:\mu \ne 180$

If the $P$-value is smaller than the significance level , then reject the null hypothesis:

$0.0589<0.10\Rightarrow Reject{H}_0$

There is enough convincing evidence that the true mean volume of liquid is different from $180$millilitres. It is observed that the conclusion changed.