Given:
To Find:
Solution:
As here in Question we are given Surface area of cube is 150 sq. feet. So, firstly we have find the side of edge of cube. Let 'a' be the edge of the cube
We know that,
Substituting the required values,
Now,
Hence,
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:
And the alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
50 tested at the null hypothesis:
This means that
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
Value of the test statistic:
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.