In: Statistics and Probability
1. A bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce the waiting time that currently is 10 minutes.
a) Formulate the hypotheses and rejection rule for this problem.
b) A random sample of 70 waiting times was obtained after the system was implemented. The sample showed a sample mean of 9.5 minutes and a standard deviation of 2.2 minutes. Obtain the p-value.
c) At alpha=.01, do you believe the new system indeed reduced the waiting time? Explain.
2. Across the states, 12.2% of all families (urban, rural, and suburban) send their children to private schools. A researcher believes that the percentage of suburban families who send their children to private schools is higher than the average for all families.
a) Formulate the hypotheses and rejection rule for this problem.
b) A nationwide sample of 1,000 suburban families showed that 162 send their children to private schools. Obtain the p-value.
c) At α = .05, would you conclude that the percentage of suburban families sending their children to private schools is higher than the percentage of all families? Explain.
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