Question 4 A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 100 homeowners selected from this area showed that they pay an average of $1875 per month for their mortgages. The population standard deviation of all such mortgages is $255. a) Give a point estimate for the mean amount of mortgage paid per month by all homeowners in this area. b) Find a 87% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area. c)Does the true population mean lie in the interval calculatedabove? (Just circle the correct answer) Yes, No cannot tell d) Answer the following for the 87% confidence interval, assuming all other values remain the same. Just circle the right answer. (i) How would the width of the confidence interval change if the confidence level increases to 95%? Would the width Increase decrease or remain the same? (ii) How would the width of the confidence interval change if the sample size n is decreased? Would the width Increase decrease or remain the same