Question

The GPA of accounting students in a university is known to be normally distributed. A random sample of 32 accounting students results in a mean of 2.97 and a standard devlation of 0.16 . Construct the 90% confidence interval for the mean GPA of all accounting students at this university. Multiple Cholce

a. 2.97±1.729(0.16/√32)
b. 2.97±1.96(0.16/√32)
c. 2.97±2.086(0.16/√32)
d. 2.97±1.696(0.16/√32)

Answer 1

To construct a 90% confidence interval for the mean GPA of all accounting students at a university, use the formula: mean ± z * (standard deviation / square root of sample size). The 90% confidence interval is 2.912 to 3.028.

Step-by-step explanation:

To construct a 90% confidence interval for the mean GPA of all accounting students at this university, we can use the formula: mean ± z * (standard deviation / square root of sample size). Here, the mean is 2.97, the standard deviation is 0.16, and the sample size is 32. To calculate the z-value for a 90% confidence level, we can refer to a standard normal distribution table or use a calculator. The z-value for a 90% confidence level is approximately 1.645. Plugging in the values, the 90% confidence interval is:

2.97 ± 1.645 * (0.16 / √32)

Simplifying this expression, we get:

2.97 ± 0.058

Therefore, the 90% confidence interval for the mean GPA of all accounting students at this university is approximately 2.912 to 3.028.