1. A random sample of 49 observations from a normal population yields a sample mean of85 with a standard deviation of 14.(a) Test the claim that the population mean differs from 81. Use a 0.05 significancelevel.(b) Test the claim that the population mean is greater than 85. Use a 0.05 significancelevel.

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 differsfrom 16?12 15 14 19 15 20 16

3. A Washington, D. C., think tank announces the typical teenager sent 50 text messagesper day in 2009. To update the estimate, you phone a sample of teenagers and ask themhow many text messages they sent the previous day. Their responses were:51 175 47 49 44 54 145 203 21 59 42 100At 0.05 level, can you conclude that the mean number is greater than 50? Estimate thep-value and describe what it tells you.

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

5. A recent article in The Wall Street Journal reported that the 30-year mortgage rate isnow less than 6%. A sample of eight small banks in the Midwest revealed the following30-year rates (in percent):4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6At 0.10 level, can you conclude that the 30-year mortgage rate is now less than 6%?