Question

University B also conducted a survey on their students’ cost of textbooks per quarter and their result of a random sample is provided below: Sample Results Sample size 400 Sample mean $150 Sample standard deviation $40 Calculate the 95% confident interval for average students’ cost of textbooks at university B

Answer 1

Using the given sample data from University B with a sample mean of $150, sample standard deviation of $40, and a sample size of 400, we calculated the 95% confidence interval for the average cost of textbooks to be between $146.08 and $153.92.

Step-by-step explanation:

The student is seeking to calculate the 95% confidence interval for the average cost of textbooks at University B using the provided sample results. With a sample size of 400, a sample mean of $150, and a sample standard deviation of $40, we can calculate the confidence interval using the formula for a confidence interval for a mean:

CI = μ ± (z* · (σ/ √ n))

Where CI represents the confidence interval, μ is the sample mean, z* is the z-score for the confidence level (for 95% confidence, z* is approximately 1.96), σ is the sample standard deviation, and n is the sample size.

Calculating this particular confidence interval:

1. First, divide the standard deviation by the square root of the sample size to get the standard error (SE): SE = $40 / √ 400 = $40 / 20 = $2.
2. Next, multiply the z-score by the standard error: 1.96 × $2 = $3.92.
3. Finally, calculate the lower and upper bounds of the confidence interval:
   

The 95% confidence interval for the average cost of textbooks at University B is thus between $146.08 and $153.92.