Respuesta :
Answer:
Pvalue of 0.0446 < 0.05, which means that we reject the null hypothesis and accept the alternative hypothesis, that the true mean is larger than the specification.
Step-by-step explanation:
The average weight of a package of rolled oats is supposed to be at most 18 ounces.
This means that the null hypothesis is:
[tex]H_{0}: \mu \leq 18[/tex]
Is the true mean larger than the specification?
Due to the question asked, the alternate hypothesis is:
[tex]H_{a}: \mu > 18[/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.
18 is tested at the null hypothesis:
This means that [tex]\mu = 18[/tex]
A sample of 18 packages shows a mean of 18.20 ounces with a sample standard deviation of 0.50 ounces.
This means that [tex]n = 18, X = 18.2, \sigma = 0.5[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{18.2 - 18}{\frac{0.5}{\sqrt{18}}}[/tex]
[tex]z = 1.7[/tex]
Pvalue of the test:
Probability of finding a sample mean above 18.2, which is 1 subtracted by the pvalue of z = 1.7.
Looking at the z-table, z = 1.7 has a pvalue of 0.9554.
1 - 0.9554 = 0.0446
0.0446 < 0.05, which means that we reject the null hypothesis and accept the alternative hypothesis, that the true mean is larger than the specification.
