A sanitation supervisor is interested in testing to see if the mean amount of ga

Question

A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 48.2 pounds and the sample standard deviation was 3.3 pounds. Conduct the appropriate hypothesis test using a 0.01 level of significance.

1) What are the appropriate null and alternative hypotheses?

a. H0: = 50 versus Ha: < 50

b. H0: = 50 versus Ha: > 50

c. H0: = 50 versus Ha: 50

d.H0: x = 50 versus Ha: x 50

2) What is the test statistic? Give your answer to four decimal places.
3) What is the P-value for the test? Give your answer to four decimal places.
4) What is the appropriate conclusion?

a. Reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.01

b. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.01.    

c. Reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.01.

d. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.01.

Explanation / Answer

a) option c

. H0: = 50 versus Ha: 50

Hgiven x^ =50

sample mean =48.5

standard deviation =3.3

n=36

df=35

alpha =0.01

b) test stastic is = x^-mean / (s/sqrtn)

=50-48.2 / 3.3(sqrt36)=1.8/0.55= 3.2727

c) p value is we look into standard z table for its a two tailed test p(3.2727)=2(p(z>3.2727)=2(1-0.9995)=2(0.0005)=0.001

d) option a

as pvalue is 0.001 <0.01

reject the claim as p value is smaller than 0.01

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