MUST EXPLAIN A&B AND SHOW ALL WORK FOR EACH.

A. A study was done to determine if humans were capable of extrasensory perception (ESP). The study included 20,000 subjects from an SRS. The results were statistically significant at the .01 level and all statistical and design methods were properly used. Can the researchers reliably conclude that ESP does exist?

B. A 95% confidence interval was computed around a sample mean of 10. The resulting confidence interval is (5, 11). Does this appear to be a valid confidence interval?

A)

Yes, the confidence interval includes the sample mean.

B)

Yes, the confidence interval is small enough to be a 95% confidence interval.

C)

No, the confidence interval should be symmetric around the sample mean.

D)

No, the confidence interval cannot contain the sample mean.

C. The scores on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed with a standard deviation of s = 10. A simple random sample of 25 children is taken, and each is given the WISC. The mean of the 25 scores is = 104.32. Based on these data, what is a 95% confidence interval for m?

A)

104.32 0.78

B)

104.32 3.29

C)

104.32 3.92

D)

104.32 19.60

D. The square footage of the several thousand apartments in a new development is advertised to be 1250 square feet, on average. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicions. Let m represent the true average area (in square feet) of these apartments. What are the appropriate null and alternative hypotheses?

A)

H₀: m = 1250 vs. H_a: m < 1250

B)

H₀: m = 1250 vs. H_a: m 1250

C)

H₀: m = 1250 vs. H_a: m > 1250

E. It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of s = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snow-covered test track. The tests resulted in a mean stopping distance of = 212.9 meters.What is the P-value?

A)

0.012

B)

0.050

C)

0.025

D)

0.006

E)

Not within 0.002 of any of the above