A bank manager wants to know the mean amount of mortgage paid per month by homeo

Question

A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 120 homeowners selected from this area showed that they pay an average of $ 1575 per month for their mortgages. The population standard deviation of such mortgages is $215. Determine: a) parameter to estimate: b) estimator: c) point estimate: d) What is the sampling distribution of your estimator? e) Find a 95% Confidence Interval (CI) for the mean amount of mortgage paid per month by all homeowners in this area f) f)What is the margin of error of estimate from part e g) Is the true population mean included in this interval? h) Is the sample mean included in this interval? I) Is this statement true: Probability (the true population mean is included in this interval above) =0.95. If not, please correct. j) What does the phase "95% confident "mean? j) Find a 97% Confidence Interval (CI) for the mean amount of mortgage paid per month by all homeowners in this area k) Suppose the confidence interval is too wide How can the width of this interval be reduced? Discuss all possible alternatives. Which alternative is the best?

Explanation / Answer

Answer:

Part a

Parameter to estimate is given as the mean amount of mortgage paid per month by homeowners in an area.

Part b

The estimator for the given study is given as population mean amount of mortgage per month. For this research study we are interested in finding the average amount of mortgage per month by the customers in the specific area.

Part c

The point estimate for the mean amount of mortgage paid per month by homeowners in an area is given as $1575 per month.

Part d

The sampling distribution of the mean amount of mortgage per month will follow an approximate normal distribution with the mean $1575 and standard deviation as given below:

Estimator for SD = Standard error = /sqrt(n) = 215/sqrt(120) = 19.62672498.

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