Question

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is $179.6$ml and the standard deviation is $1.3$ml. A significance test yields a $P$-value of $0.0589$. Interpret the $P$-value.

Short answer

There is a $5.89\%$possibility that the mean volume of liquid in a sample of $40$bottles is $179.6$millilitres or more extreme, when the mean volume of liquid of all bottles is$180$ millilitres

Step-by-step solution

Step 1:Given information

The mean amount of liquid in the bottles is $179.6$$\mathrm{ml}$and the standard deviation is $1.3\mathrm{ml}$. A significance test yields a$P$-value of $0.0589$

Step 2:Explaination

$P=0.0589=5.89\%$

$\overline{x}=179.6$

$s=1.3$

Claim is mean is $180$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population mean 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.

$H_0:\mu =180$

$H_a:\mu \ne 180$

The P-value is the probability of getting the value of the test static or a value more extreme, when the null hypothesis is true.

There is a $5.89\%$possibility that the mean volume of liquid in a sample of 40 bottles is $179.6$millilitres or more extreme, when the mean volume of liquid of all bottles is$180$ millilitres