MATH 200 University of California The Average Iq Among Adults Questions

Show ALL work and use appropriate notation. If using a calculator, state the programs

and/or commands you are using. Round ALL answers to three decimal places, where

appropriate.

1. Suppose you want to test the claim that ?? ? 0. 24 at the ? = 0. 02 significance level. Find

the appropriate critical value(s) for this test. (6pts)

2. A 95% confidence interval for the average IQ among adults is (97.1, 101.9).

a. What is the best guess for the average IQ among adults? (4pts)

b. What is the margin of error for the average IQ among adults? (4pts)

3. Suppose you wish to estimate the proportion of cars that are black. Find the sample size

needed to assure with 92% confidence that the sample proportion will not differ from the

population proportion by more than 3%. (8pts)

4. A study of 18 python snakes found the average length was 22.4 ft. Find the margin of error

needed to estimate the average length of all python snakes with 90% confidence. Assume ?

is known to be 3.2 ft. (8pts)

5. A sample of 25 statistics students had an average test score of 82.1 and standard deviation of

6.4. Use this information to construct a 95% confidence interval estimate of the population

standard deviation. Round your final answer to one decimal place. (8pts)

6. CalTrans claims the average speed at 4pm on a particular freeway is faster than 62mph.

When ten vehicles were observed at random for their speeds (in mph) on a particular stretch

of freeway, the following data was obtained: 68, 78, 69, 61, 68, 65, 60, 64, 60, 62. Assume

vehicle speed is normally distributed.

a. State the hypotheses and identify the claim. (3pts)

b. Calculate the test statistic and p-value. (4pts)

c. State your conclusion based on the ? =. 10 significance level. What does this say

about CalTrans claim? (4pts)

7. The U.S. Mint claims the coins they make are “fair”. A random coin was flipped and the

results were 278 heads and 322 tails.

a. State the hypotheses and identify the claim. (3pts)

b. Calculate the test statistic and p-value. (4pts)

c. State your conclusion based on theTest the claim at the 0.05 significance level. What

does this say about the coins made by the U.S. Mint? (4pts)