A bank manager wants to know the mean amount of mortagage paid per month by home

Question

A bank manager wants to know the mean amount of mortagage 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. a. Find a 97% confidence interval the mean amount of mortgage paid per month by all homewners in this area. b. Suppose the confidence interval obtained in part a is too wide. How can uic this interval be reduced? Discuss possible alternatives. Which alternative is best.

Explanation / Answer

Here we have to find 97% confidence interval for mean amount of mortage paid pper month by all homeowners in this area.

97% confidence interval for mean is,

Xbar - E < mu < Xbar + E

Here we use Z-interval because population standard deviation is given.

This confidence interval we can find by using TI-83 calculator.

Given values are :

Xbar = $ 1575

sigma = $215

n = 120

C-level = 97% = 0.97

steps :

STAT --> 7:ZInterval --> ENTER --> HIghlight on Stats --> ENTER --> Input sigma, Xbar,n and C-level --> Calculate --> ENTER

Output is :

97% confidence interval for mean is (1532.4, 1617.6).

Conclusion: We are 97% confident that the population mean is lies between 1532.4 and 1617.6.

We have to decrease confidence level so that the confidence interval is narrower.

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