1. A random sample of 49 observations from a normal population yields a sample mean of 85 with a standard deviation of 14.

(a) Test the claim that the population mean differs from 81. Use a 0.05 significance level.

(b) Test the claim that the population mean is greater than 85. Use a 0.05 significance level.

2. The following data were sampled from a normally distributed population. At the 10% significance level, is there evidence to indicate that the mean of the population differs from 16?

12 15 14 19 15 20 16

3. A Washington, D. C., "think tank" announces the typical teenager sent 50 text messages per day in 2009. To update the estimate, you phone a sample of teenagers and ask them how many text messages they sent the previous day. Their responses were:

51 175 47 49 44 54 145 203 21 59 42 100

At 0.05 level, can you conclude that the mean number is greater than 50? Estimate the p-value and describe what it tells you.

4. The National Safety Council reported that 52% of American turnpike drivers are men. A sample of 300 cars traveling southbound on the New Jersey Turnpike yesterday revealed that 170 were driven by men. At the 0.01 significance level, can we conclude that a large a larger proportion of men were driving on the New Jersey Turnpike than the national statistics indicate?

5. A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now less than 6%. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent):

4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6

At 0.10 level, can you conclude that the 30-year mortgage rate is now less than 6%