For each of the following problems: determine whether it is a mean or proportion, then construct and interpret a 95% confidence interval for each.

Watch the language; Anything which gives you a percentage as a sample result is about a proportion, or when they say __ out of the ____ responded with... also a proportion.

Problems about a mean/average will also include a standard deviation. The numbers in the problems for a mean cannot be changed as you might for proportions to change them to percentages.

Calculator:

Proportions:

STAT TESTS A: 1-PropZInt

x = successes

n = total number of observations/sample size

C-level must be entered as a decimal (i.e. 95% = 0.95)

Means:

STAT TESTS 8: TInterval

x = sample mean/average

Sx = sample standard deviation

n = total number of observations/sample size

C-level must be entered as a decimal

We are 95% confident that the interval from ___ to ___ captures the true (mean/proportion) of (context of the problem).

1. A college professor wants to know how effective he is in the eyes of his students. He gives a questionnaire to all of his students and randomly selects 40 to assess. Of the 40 selected questionnaires, 27 of the students agreed that his teaching methods were effective. Use this information to estimate with 95% confidence the true proportion of this professor's students who believe he is an effective teacher.

2. The Fish and Gaming Commission is concerned at the growing number of fish which have died in a lake at a state park in Utah. If the carbon dioxide levels are too high the park must take action to save the wildlife. 45 random samples of water were taken from various spots within the lake, and the average CO2 reading was 2.3 mg/L with a standard deviation of 0.2. Estimate the lake's true carbon dioxide level with 95% confidence from this information.

3. A track coach is trying to get an idea of how fast his 4x4 team should run the relay, so he randomly selects 20 schools and sends scouts to one of their track meets. He found that the average time to be 3 minutes and 45 seconds (225 seconds) with a standard deviation of 23 seconds. Estimate the true average 4x4 time for these schools with 95% confidence.

4. For their stats project, two students decided to estimate the proportion of drivers which do a rolling stop through stop signs (a rolling stop is when drivers slow down but never actually stop.) They randomly choose some intersections and record a total of 60 cars, of which 36 engaged in a rolling stop. Use this information to estimate the proportion of drivers who do a rolling stop through stop signs with 95% confidence.