Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A 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 visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
