T Test - Testing of hypothesis using five step procedure

1. The new director of special programs in XYZ Corporation felt the customers were waiting too long to receive and complete forms needed to enroll in special programs. After collecting some data, Ms. Jones determined the mean wait time was 28 minutes. She felt this time period was excessive and she instituted new procedures to streamline the process. One month later, a sample of 127 customers was selected. The mean wait time recorded was 26.9 minutes and the standard deviation of the sampling was 8 minutes. Using the 0.02 level of significance, conduct a five-step hypothesis testing procedure to determine if the new processes significantly reduced the wait time.

2. A study was conducted on the annual incomes of corporate trainers in the state of New York in metropolitan areas having a population less than 100,000 and in metropolitan areas having a population over 500,000. Some sample statistics are:
SAMPLE STATISTIC POPULATION LESS THAN 100K POPULATION MORE THAN 500K
Sample Size 45 60
Sample Mean $31,290 $31,330
Sample SD $1,060 $1,900
Test the hypothesis that the annual income of corporate trainers in areas of more then 500,000 are significantly more than those in areas of less than 100,000. Use the 5% level of risk.

3. In a recent national survey, the mean weekly allowance for a nine-year-old child from his or her parents was reported to be $3.65. A random sample of 45 nine-year-olds in northwestern Ohio revealed the mean allowance to be $3.69 with a standard deviation of 0.24. At the 0.05 level of significance, is there a difference in the mean allowances nationally and the mean allowances in northwestern Ohio for nine-year-olds?

4. Metro Real Estate Association is preparing a pamphlet that they feel might be of interest to prospective homebuyers in the Middletown and Brockton areas of the city. One item of interest is the number of years children remain in the same district for schooling. A sample of 40 households with school-aged children in Middletown was randomly selected. The mean length of time in the district was 7.6 years, with a standard deviation of 2.3 years. A sample of 55 households in Brockton revealed the mean length of time in the district was 8.1 years, with a standard deviation of 2.9 years. At the 0.05 level of significance, can we conclude the Middletown students stayed in their districts less time than the Brockton students? Use the five-step hypothesis testing procedure.

5. A sample of 40 observations is selected from one somewhat normal population. The sample mean is 102 and the sample standard deviation is 5. A sample of 50 observations is selected from a second source. The sample mean was 99 and the standard deviation was 6. Conduct a test of the hypothesis using the 0.04 level of significance.