Respuesta :
Answer:
No, there is not sufficient evidence to support the claim that the bags are underfilled
Step-by-step explanation:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 434[/tex]
It is believed that the machine is underfilling the bags.
This means that the alternate hypothesis is:
[tex]H_{a}: \mu < 434[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
434 is tested at the null hypothesis:
This means that [tex]\mu = 434[/tex]
A 9 bag sample had a mean of 431 grams with a variance of 144.
This means that [tex]X = 431, n = 9, \sigma = \sqrt{144} = 12[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{431 - 434}{\frac{12}{\sqrt{9}}}[/tex]
[tex]z = -0.75[/tex]
P-value of the test:
The pvalue of the test is the pvalue of z = -0.75, which is 0.2266
0.2266 > 0.01, which means that there is not sufficient evidence to support the claim that the bags are underfilled.
