High School

A hybrid course is one that contains both online and classroom instruction. In a study performed 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 43 students, the mean number of hours was 80.7, with a standard deviation of 51.7.

(a) Construct a 99.5% confidence interval for the mean number of hours it takes for a student to meet course objectives. Round the answers to one decimal place.

A 99.5% confidence interval for the mean number of hours it takes for a student to meet the course objectives is: _______.

Answer :

Part 1 of 2 -

(a) 99.5% confidence interval - 576.7 to 985.1 hours.

Part 2 of 2 -

(b) Interval would be narrower with a larger sample size.

How to compute the above interval and sample

Part 1 of 2 -

(a) To construct a 99.5% confidence interval for the mean number of hours, we can use the formula -

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

Where Z is the critical value corresponding to the desired confidence level.

For a 99.5% confidence level, the critical value Z can be obtained from a standard normal distribution table or using a statistical calculator. The Z value for a 99.5% confidence level is approximately 2.807.

Using the given data -

Mean = 80.9

Standard Deviation = 51.6

Sample Size = 43

Confidence Interval = 80.9 ± (2.807 * (51.6 / √43))

Calculating the confidence interval gives -

Confidence Interval = 80.9 ± 104.2

So, the 99.5% confidence interval for the mean number of hours is 576.7 to 985.1.

Part 2 of 2 -

(b) If a sample of 50 students had been studied, the interval would be narrower than the one constructed in part (a).

With a larger sample size, the estimate of the mean becomes more precise, resulting in a narrower confidence interval.

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Full Question:

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Software instruction: A hybrid course is one that contains both online and classroom instruction. In a study performed 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 43 students, the mean number of hours was 80.9, with a standard deviation of 51.6. Part 1 of 2 (a) Construct a 99.5% confidence interval for the mean number of hours it takes for a student to meet course objectives, Round the answers to one decimal place. A 99.5% confidence interval for the mean number of hours it takes for a student to meet the course objectives is 576 << 104.2 Part: 1 / 2 Part 2 of 2 (b) If a sample of 50 students had been studied, would you expect the interval to be wider or narrower than the interval constructed in part (a)? Explain. The confidence interval would be (Choose one) than the interval constructed in part (a).

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