# Confidence Interval Homework

**Introduction to Statistics Spring/Summer 2020**

**Confidence Interval**

**For each problem, round to the nearest tenth or hundredth. Ten points.**

A sample of Alzheimer’s patients are tested to assess the amount of time in stage IV sleep. It has been hypothesized that individuals suffering from Alzheimer’s Disease may spend less time per night in the deeper stages of sleep. Number of minutes spent in Stage IV sleep is recorded for sixty-one patients. The sample produced a mean of 48 minutes (S=14 minutes) of stage IV sleep over a 24-hour period. Compute a 99 percent confidence interval for this data. What does this information tell you about an individualâ€™s (an Alzheimer’s patient) stage IV sleep?

A university wants to know more about the knowledge of students regarding international events. The university is concerned that their students are uninformed in regards to news from other countries. A standardized test is used to assess studentsâ€™ knowledge of world events (national reported mean=65, S=5). A sample of 30 students are tested (sample mean=58, Standard Error=3.2). Compute a 95 percent confidence interval based on this sample’s data. How do these students compare to the national sample?

A sample of students from an introductory psychology class were polled regarding the number of hours they spent studying for the last exam. All students anonymously submitted the number of hours on a 3 by 5 card. There were 24 individuals in the one section of the course polled. The data was used to make inferences regarding the other students taking the course. There data are below:

4.5 | 22 | 7 | 14.5 | 9 | 9 | 3.5 | 8 | 11 | 7.5 | 18 | 20 |

7.5 | 9 | 10.5 | 15 | 19 | 2.5 | 5 | 9 | 8.5 | 14 | 20 | 8 |

Compute a 90 percent confidence interval. What does this tell us?

An independent agency has been charged with investigating gender discrimination based on pay differentials in a large company. They find that from a sample of 236 women in salaried positions, women are paid an average of 48,352 dollars annually with a standard deviation of 5,285 dollars. From a sample of 257 men, they find that men in salaried positions on average earn about 54,285 dollars annually with a standard deviation of 8,456 dollars.

- Calculate a 95 percent confidence interval for women.
- What does this mean?
- Calculate a 95 percent confidence interval for men.

- What does this mean?
- What can we conclude about gender discrimination in this company from the calculations above?

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