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# Confidence Intervals and Introduction to Inference Review Problems for AP Statistics

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By — McGraw-Hill Professional
Updated on Feb 4, 2011

Review the following concepts if necessary:

### Problems

1. Use a normal approximation to the binomial to determine the probability of getting between 470 and 530 heads in 1000 flips of a fair coin.
2. A survey of the number of televisions per household found the following probability distribution:
3. What is the mean number of television sets per household?

4. A bag of marbles contains four red marbles and five blue marbles. A marble is drawn, its color is observed, and it is returned to the bag.
1. What is the probability that the first red marble is drawn on trial 3?
2. What is the average wait until a red marble is drawn?
5. A study is conducted to determine which of two competing weight-loss programs is the most effective. Random samples of 50 people from each program are evaluated for losing and maintaining weight loss over a 1-year period. The average number of pounds lost per person over the year is used as a basis for comparison.
1. Why is this an observational study and not an experiment?
2. Describe an experiment that could be used to compare the two programs. Assume that you have available 100 overweight volunteers who are not presently in any program.
6. The correlation between the first and second statistics tests in a class is 0.78
1. Interpret this value.
2. What proportion of the variation in the scores on the second test can be explained by the scores on the first test?

### Solutions

1. Let X = the number of heads. Then X has B(1000, 0.5) because the coin is fair. This binomial can be approximated by a normal distribution with mean = 1000(0.5) = 500 and standard deviation
2. .

Using the TI-83/84 calculator, normalcdf (–1.9,1.9).

3. μx = 0(0.3) + 1(0.37) + 2(0.46) + 3(0.10) + 4(0.04) = 1.75.
4.
1. P(draw a red marble) = 4/9
.
2. Average wait
.
5.
1. It is an observational study because the researchers are simply observing the results between two different groups. To do an experiment, the researcher must manipulate the variable of interest (different weight-loss programs) in order to compare their effects.
2. Inform the volunteers that they are going to be enrolled in a weight-loss program and their progress monitored. As they enroll, randomly assign them to one of two groups, say Group A and Group B (without the subjects' knowledge that there are really two different programs). Group A gets one program and Group B the other. After a period of time, compare the average number of pounds lost for the two programs.
6.
1. There is a moderate to strong positive linear relationship between the scores on the first and second tests.
2. 0.782 = 0.61. About 61% of the variation in scores on the second test can be explained by the regression on the scores from the first test.

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