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.What are the appropriate null and alternative hypotheses?A. H0: x = 50 versus Ha: x ? 50B. H0: ? = 50 versus Ha: ? ? 50 C. H0: ? = 50 versus Ha: ? < 50D. H0: ? = 50 versus Ha: ? > 50

Answer 1

Answer: $H_0 : \mu=50\\\\ H_1 : \mu\neq50$

Step-by-step explanation:

An null hypothesis ($H_0$) is a statement of equality which shows that there is no statistical difference between the groups being tested.

An alternative hypothesis  ($H_1$) is a statement of inequality which shows that there is statistical difference between the groups being tested.

Let $\mu$ be the population mean amount of garbage per bin .

Given : A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50.

i.e. $\mu\neq 50$ → Alternative

Thus , the appropriate null and alternative hypotheses :

$H_0 : \mu=50\\\\ H_1 : \mu\neq50$