A homeowner is travelling overseas long-term and wants to rentout his house. A local management company advises the home-ownerthat average rental income for houses like his in this area, i.e. 3bedroom semi-detached town house, is no more than 770 euro. Thehomeowner thinks that it is more than this. He notices a report inthe local paper in which a random sample of 13 rental properties ofthis type, in this area, gave an average of 871.51 euro with astandard deviation of 82.74 euro. Is this evidence that the averagerental income of houses of this type in this area is greater than770 euro? To answer this, test the following hypotheses atsignificance level ? = 0.05 H 0: ? = 770 H a: ? > 770.

Fill in the blanks in the following:

An estimate of the population mean is.

The standard error is .

The distribution is (examples: normal / t12 / chisquare4/ F5,6).

The test statistic has value TS=.

Testing at significance level ? = 0.05, the rejectionregion is: (less/greater) than (2 dec places).

Since the test statistic (is in/is not in) therejection region, there (is evidence/is noevidence) to reject the null hypothesis, H 0.

There (is sufficient/is insufficient) evidenceto suggest that average rental income for houses like his in thisarea, i.e. 3 bedroom semi-detached town house, ?, is greater than770 euro.

Were any assumptions required in order for thisinference to be valid?

a: No - the Central Limit Theorem applies, which states thesampling distribution is normal for any populationdistribution.

b: Yes - the population distribution must be normallydistributed. Insert your choice (a or b):