Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Answer:
We accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.
Step-by-step explanation:
A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 50[/tex]
And the alternate hypothesis is:
[tex]H_{a}: \mu \neq 50[/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.
50 tested at the null hypothesis:
This means that [tex]\mu = 50[/tex]
In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.
This means that [tex]n = 36, X = 50.67, \sigma = 3.9[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{50.67 - 50}{\frac{3.9}{\sqrt{36}}}[/tex]
[tex]z = 1.03[/tex]
p-value:
Since we are testing if the mean is differente from a value and the z-score is positive, the pvalue is 2 multipled by 1 subtracted by the pvalue of z = 1.03.
z = 1.03 has a pvalue of 0.8485
1 - 0.8485 = 0.1515
2*0.1515 = 0.3030
0.3030 > 0.01, which means that we accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
