According to Moebs Services Inc., an individual checking account at major U.S. banks costs these banks between $350 and $450 per year (Time, November 21, 2011). Suppose that the average cost of individual checking accounts at major U.S. banks was $400 for the year 2011. A bank consultant wants to determine whether the current mean cost of such checking accounts at major U.S. banks is more than $400 a year. A recent random sample of 150 such checking accounts taken from major U.S. banks produced a mean annual cost to them of $410. Assume that the standard deviation of annual costs to major banks of all such checking accounts is $60.
a. Find the p-value for the test of hypothesis. Based on this p-value, would you reject the null hypothesis if the maximum probability of Type I error is to be .05? What if the maximum probability of Type I error is to be .01?
b. Test the hypothesis of part a using the critical-value approach and α = .05. Would you reject the null hypothesis? What if α = .01? What if α = 0?