Question

A homeowner is travelling overseas long-term and wants to rent out his house. A local management company advises the home-owner that average rental income for houses like his in this area, i.e. 3 bedroom semi-detached town house, is no more than 770 euro. The homeowner thinks that it is more than this. He notices a report in the local paper in which a random sample of 13 rental properties of this type, in this area, gave an average of 871.51 euro with a standard deviation of 82.74 euro. Is this evidence that the average rental income of houses of this type in this area is greater than 770 euro? To answer this, test the following hypotheses at significance level α = 0.05 H 0: μ = 770 H a: μ > 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 α = 0.05, the rejection region is: (less/greater) than (2 dec places).

Since the test statistic (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H 0.

There (is sufficient/is insufficient) evidence to suggest that average rental income for houses like his in this area, i.e. 3 bedroom semi-detached town house, μ, is greater than 770 euro.

Were any assumptions required in order for this inference to be valid?

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

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

Answer 1

To test against

Here

sample mean

sample standard deviation

and sample size

The standard error is

The test statistic can be written as

which under H₀ follows a t distribution with n -1 df.

We reject H₀ at 5% level of significance if

The distribution is : t₁₂

The value of the test statistic t_obs= 4.42349

The rejection region is :

or

Since the test statistic is in the rejection region, there is evidence to reject the null hypothesis, H₀.

There is sufficient evidence to suggest that average rental income for houses like his in this area, i.e. 3 bedroom semi-detached town house, μ, is greater than 770 euro.

Assumptions required in order for this inference to be valid :

ans-> Yes - the population distribution must be normally distributed.