Respuesta :
Answer:
There is not enough evidence to conclude that the bags of potato chips are underfilled.
Step-by-step explanation:
In this case we need to determine whether the bag filling machine works correctly at the 415 gram setting.
The hypothesis can be defined as follows:
H₀: The bags of potato chips are not underfilled, i.e. μ = 415.
Hₐ: The bags of potato chips are underfilled, i.e. μ < 634.
The information provided is:
[tex]n=44\\\bar x=410\\\sigma=\sqrt{729}=27\\\alpha=0.05[/tex]
As the sample size is quite large, i.e. n = 44 > 30 and is taken form an unknown population, according to the Central limit theorem the sampling distribution of sample mean will follow the Normal distribution.
So, a z-test for single mean will be applied to perform the test.
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{SD/\sqrt{n}}\\\\=\frac{410-415}{27/\sqrt{44}}\\\\=-1.23[/tex]
The test statistic value is -1.23.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the one-tailed test as follows:
[tex]p-value=P(Z <-1.23)\\=0.10935[/tex]
*Use a z-table for the probability.
The p-value of the test is 0.10935.
p-value = 0.10935 > 0.05
The null hypothesis will not be rejected.
Thus, there is not enough evidence to conclude that the bags of potato chips are underfilled.
