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: x = 50 versus Ha: x ? 50
H0: ? = 50 versus Ha: ? ? 50
H0: ? = 50 versus Ha: ? < 50
H0: ? = 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.
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 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.
Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.05.