Question

1. For each question state
   1. whether we have one sample or two samples and if we have two samples identify whether they are independent or matched pairs
   2. define the parameter(s) of interest
   3. state the null and alternative hypothesis using statistical notations such as µ for one population mean, µ₁ and µ₂ for two independent population means, µ_D for the mean of difference within pair.
      1. The administrator at your local hospital states that on weekends the average wait time for emergency room visits is 10 minutes on average. Based on discussions you have had with friends who have complained about how long they waited to be seen in the emergency room over a weekend, you decided to test whether the average wait time is greater than the administrator’s claim. You randomly surveyed 30 people who visited the emergency room recently and found the sample mean waiting of 13 minutes and a sample standard deviation of 5 minutes.
      2. In a data analysis study conducted by personnel at the Statistics Consulting Center at Virginia Tech, two different materials, alloy A and alloy B were compared in terms of breaking strength. Alloy A is more expensive, but it should certainly be adopted if it can be shown to be stronger than alloy B. To test whether alloy A is indeed stronger than alloy B on average, random samples of beams made from each alloy were selected, and strength was measured in units of 0.001-inch deflection as a fixed force was applied at both ends of the beam. Twenty specimens were used for each of the two alloys.
      3. Forty-four sixth graders were randomly selected from a school district. Then, they were divided into 22 matched pairs, each pair having equal IQ’s. One member of each pair was randomly selected to receive special training. Then all of the students were given an IQ test. The researcher wants to test if special training has any effect.

Answer 1