a random sample of 75 students at the university of minnesota spend an average of $614 per month in rent…

a random sample of 75 students at the university of minnesota spend an average of $614 per month in rent with a standard deviation of $219. the distribution is moderately skewed to the high end. which of the following statements are true?\n\ni. 95% of students at the university spend $564 to $664 on rent.\nii. we are 95% confident that the average rent for students at the university is between $564 and $664.\niii. because we cannot examine other characteristics of the students in the random sample, it is not advisable to construct a confidence interval.\n\no i only\no ii only\no iii only\no i and ii\no i, ii, and iii

a random sample of 75 students at the university of minnesota spend an average of $614 per month in rent with a standard deviation of $219. the distribution is moderately skewed to the high end. which of the following statements are true?\n\ni. 95% of students at the university spend $564 to $664 on rent.\nii. we are 95% confident that the average rent for students at the university is between $564 and $664.\niii. because we cannot examine other characteristics of the students in the random sample, it is not advisable to construct a confidence interval.\n\no i only\no ii only\no iii only\no i and ii\no i, ii, and iii

Answer

Explanation:

Step1: Recall confidence - interval concept

A confidence interval gives a range of values for the population parameter (in this case, the average rent of all students at the university) based on sample statistics. It does not mean that a certain percentage of individual data points lie within that range.

Step2: Analyze statement i

The statement "95% of students at the university spend $564 to $664 on rent" is incorrect. A confidence interval is for the population mean, not for individual data - points.

Step3: Analyze statement ii

For a large sample size ($n = 75$), we can construct a confidence interval for the population mean. The formula for a confidence interval for the population mean when the population standard - deviation $\sigma$ is unknown (we use the sample standard - deviation $s$ instead) is $\bar{x}\pm t_{\alpha/2}\frac{s}{\sqrt{n}}$. For a 95% confidence interval and a large sample, we are 95% confident that the true population mean (average rent for all students at the university) lies within the calculated interval. If the calculated 95% confidence interval is ($564,664$), then we are 95% confident that the average rent for students at the university is between $564 and $664.

Step4: Analyze statement iii

We do not need to examine other characteristics of the students in the sample to construct a confidence interval for the mean rent. As long as the sample is a random sample, and the sample size is reasonably large (or the population is normally distributed), we can construct a confidence interval for the population mean. So, this statement is incorrect.

Answer:

B. ii only