4. The National Safety Council reported that 52% of American turnpike drivers ar

Question

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%?

Explanation / Answer

a) H0: p = 0.52

Ha: p >0.52

Sample proportion = 170/300 = 0.567

Standard error = Sqrt(0.52*0.48/300) = 0.028844

Z = (0.567-0.52)/0.028844 = 1.6179

Critical value at 0.01 level is 2.326

Since calculated z is less than critical value, we failed to reject the null hypothesis and conclude that there is not sufficient evidence to conclude that a large a larger proportion of men were driving on the New Jersey Turnpike than the national statistics indicate

Q5)

H0: u >= 6

Ha: u<6

sample mean = 5.6375

Sample Standard deviation = 0.63457

t =((5.6375-6)/0.63457)*Sqrt(8) = -1.61575

critical value at 0.10 level is -1.41492

Since calculated t test statistics is less than critical value, we reject the null hypotheis and conclude that  the 30-year mortgage rate is now less than 6%

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