1. A psychic was tested for ESP. The psychic was presented with 400 cards face down and was asked to determine if the card was one of four symbols: a cross, a star, a circle, or a square. The psychic was correct in 120 of the cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial.

Using the results above, construct a 99% confidence interval for p.

A. (.255, .345)

B. (.262, .338)

C. (.241, .359)

D. (.259, .341)

E. We can assert that p = 0.25 with 100% confidence because the psychic is just guessing.

2. There was an SRS of 100 flights on a large airline (airline 1) that showed that 64 of the flights were on time. An SRS of 100 flights of another large airline (airline 2) showed that 80 of the flights were on time. Let p₁and p₂be the proportion of all flights that are on time for these two airlines.

What is a 95% confidence interval for the difference p₁-p₂?

A.(-.222, -.098)

B. (-.263, -.057)

C. (-.218, -.102)

D. (-.283, -.038)

E. (.098, .222)

3. A company advertises that by using their SAT math prep class, students can increase their score by at least 50 points, A teacher is skeptical of this claim. Supposerepresents the actual mean increase in math SAT scores of the population who have used the method and assume the distribution of their scores is approximately normal. The teacher collects a data sample of 16 students who took the class to see if the claim is true. The mean increase of scores is 45 points with a standard deviation of 20 points. Is this data enough evidence that the mean improvement is less than 50 points?

H₀:= 50

H₁:A< 50

The above data are the differences in SAT scores obtained by a student before the training and after the training. What is this an example of?