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###### Math · Statistics And Probability
Question details

A random sample of single occupancy dorm rooms from the University was obtained. The size of each room (in square feet) is here

 University Dorms (sq ft) 175 182 165 204 212 169 171 178 174 134 171 196 196 127 200 178 172 186 155 146 211 154 181 152 146 193 174 147 154

(1)Find a point estimate for the mean area of single occupancy dorm rooms at this university. Round your final answer to TWO decimal places.

(2)Find the standard error of the sample mean.Round your final answer to THREE decimal places.

(3)Find the margin of error for the 95% C.I. for mean area of single occupancy dorm rooms at this University. Round your final answer to TWO decimal places.

(4)Construct and interpret a 95% C.I. for the mean area of single occupancy dorm rooms at this University.Report your LOWER LIMIT for the CI rounded to TWO decimal places.

(5)Construct and interpret a 95% C.I. for the mean area of single occupancy dorm rooms at this University. Report your UPPER LIMIT for the CI rounded to TWO decimal places.

(6)Substantial construction of new residence halls has occurred since this study was done. Find the required sample size to estimate the new mean area of standard dorm rooms within 10 square feet of the true mean by using a 99% confidence interval. Assume a standard deviation of 20 square feet.