The Mystery of College Students' Textbook Spending

How much do college students typically spend on textbooks per session?

A poll of 75 randomly selected college students showed that the students spent an average of $230 on textbooks per session. But is this amount accurate for most college students?

Answer:

Based on the given information, the 99% confidence interval for the amount of money spent by college students on textbooks is $212.57 to $247.43. The corresponding z-score is 2.575.

To calculate the confidence interval, we will use the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

where Z is the critical value corresponding to the desired confidence level, and the Standard Error is calculated as the standard deviation divided by the square root of the sample size.

Given that the sample mean is $230, the standard deviation is $55, and the sample size is 75, we can calculate the Standard Error as:

Standard Error = Standard Deviation / √Sample Size

Standard Error = $55 / √75

Standard Error ≈ $6.3246

Next, we determine the critical value Z for a 99% confidence level. From the z-table, the corresponding value is approximately 2.575.

Plugging the values into the confidence interval formula:

Confidence Interval = $230 ± (2.575 * $6.3246)

Confidence Interval ≈ $230 ± $16.2674

Therefore, the 99% confidence interval for the amount of money spent by college students on textbooks is approximately $212.57 to $247.43.

The z-score based on the sample statistics is 2.575, which corresponds to the critical value used to calculate the confidence interval. The z-score represents the number of standard deviations the sample mean is from the population mean. It is used to determine the level of confidence and establish the range of values within the confidence interval. In this case, the z-score helps us capture 99% of the possible values within the confidence interval.