Mathematics - Statistics Homework 4

Confidence Intervals

Dr. Maria Paino

Reminder, the two main formulas for SE:

SE for proportions

SE for means

1. A random sample of 429 college students was interviewed about a number of matters. For each of the below, write a sentence summarizing the results (i.e “I am 95% confident that….”)

a. They reported that they had spent an average of $378.23 on textbooks during the previous semester. If the sample standard deviation for these data is $15.78, construct an estimate of the population mean at the 95% confidence level.

b. They also reported that they had visited the health clinic an average of 1.5 times a semester. If the sample standard deviation is 0.3, construct an estimate of the population mean at the 95% confidence level.

c. On average, the sample had missed 2.8 days of classes per semester because of illness. If the sample standard deviation is 1.0, construct an estimate of the population mean at the 95% confidence level.

d. On average, the sample had missed 3.5 days of classes per semester for reasons other than illness. If the sample standard deviation is 1.5, construct an estimate of the population mean at the 95% confidence level.

2. A random sample of 500 residents of New York City shows that exactly 50 of the respondents had been victims of violent crime over the past year. Estimate the proportion of victims for the population as a whole (the confidence interval) using a 90% confidence level. Write a sentence summarizing the results (i.e “I am 95% confident that….”)

(HINT: Calculate the sample proportion. Remember that proportions are equal to frequency divided by N.)

3. A random sample of 324 residents of a community revealed that 30% were very satisfied with the quality of the education system. At the 99% level, what is your estimate of the proportion of ALL residents who are satisfied with the quality of the education system? Write a sentence summarizing the results (i.e “I am 95% confident that….”)