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 49.01 pounds and the sample standard deviation was 3.7 pounds. Conduct the appropriate hypothesis test using a 0.05 level of significance.

a) What are the appropriate null and alternative hypotheses?

H0: = 50 versus Ha: < 50H0: = 50 versus Ha: > 50    H0: x = 50 versus Ha: x 50H0: = 50 versus Ha: 50

b) What is the test statistic? Give your answer to four decimal places.   

c) What is the P-value for the test? Give your answer to four decimal places.   I got 0.1174 but is Wrong !

d) What is the appropriate conclusion?

Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.05.Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.05.    Reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.05.Reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.05.

Explanation / Answer

a) H0: = 50 versus Ha: 50

b)

here std error =std deviaiton/(n)1/2 =3.7/(36)1/2 =0.6167

therefore test statistic t=(X-mean)/std error =(49.01-50)/0.6167=-1.4595

for above test statistic ; p value =0.1444

d)Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.05.

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