High School

A hybrid course contains both online and classroom instruction. In a study at Middle Georgia State College, a software package was used as the main source of instruction in a hybrid college algebra course. The software tracked the number of hours it took for each student to meet the objectives of the course. In a sample of 42 students, the mean number of hours was 80.3, with a standard deviation of 51.7.

(a) Construct a 90% confidence interval for the mean number of hours it takes for a student to meet course objectives. Round the answers to one decimal place.

Answer :

The 90% confidence interval for the mean hours to meet course objectives is about 789.9 to 816.1 hours, based on a sample mean of 803 and standard deviation of 51.7 from 42 students.

The formula for calculating the confidence interval for a population mean with a known standard deviation is given by:

Confidence Interval = Mean ± (Z * (Standard Deviation / √Sample Size))

In this case, you have:

Mean = 803

Standard Deviation = 51.7

Sample Size = 42

Z-value for a 90% confidence level ≈ 1.645

Substitute these values into the formula:

Confidence Interval = 803 ± (1.645 * (51.7 / √42))

Now calculate the values:

Confidence Interval = 803 ± (1.645 * (51.7 / 6.4807))

Confidence Interval = 803 ± 13.1342

Rounded to one decimal place:

Confidence Interval ≈ (789.9, 816.1)

So, the 90% confidence interval for the mean number of hours it takes for a student to meet the course objectives is approximately (789.9, 816.1) hours.

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