Question

An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.5 years of the population mean. Assume the population of ages is normally distributed. (a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.6 years. (b) The sample mean is 20 years of age. Using the minimum sample size with a 90% level of confidence, does it seem likely that the population mean could be within 9% of the sample mean? within 10% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table. Click here to view page 2 of the Standard Normal Table. students. (a) The minimum sample size required to construct a 90% confidence interval is (Round up to the nearest whole number.) (b) The 90% confidence interval is ( , ). It seem likely that the population mean could be within 9% of the sample mean because 9% off from the sample mean would fall the confidence interval. It seem likely that the population mean could be within 10% of the sample mean because 10% off from the sample mean would fall the confidence interval. (Round to two decimal places as needed.)

Answer 1

Sol a) Minimum sample size estimating u with given by [8Z012 teqt be required for confidence coefficient (1-2) is OSOSODOBLOOOOOO INHIMILLI where E= permissible estos significant value of 2 24 2 11.6 X 1.6457 1.5 n- 3.078 UUU =) (n = 4 b) 90% confidence Intuval is t - stalent 's a M L X + Adla nie 20-2.353 x 1.5 L M L 200 2.353x1.5

T 118.24. u 21.76 It does not seem likely that the population mean could be within 90% of the sample mean because 9% off from the samiple mean would fall in outside the confidence intuvalo It doesnot seems likely that the population mean could be within the 10% of the sample mean because 10% off from the sample mean would fall outside the confidence Interval