In order to receive a merit raise a computer clerk must average 15 minutes or less per order form processed. An across-the-board raise was given if the average is 15 minutes or less. The supervisor randomly selects 36 order forms and carefully times the length of time required to enter all of the data on each form. The average time to enter the 36 order forms is 14.36 minutes, and the population standard deviation is 3.03 minutes with a normal distribution. Assume a confidence level of 97.5%. Follow the following multi-part format to answer the question whether a merit raise should be given. You are allowed to use PHStat2 or Excel for this question. Attach the output from Excel/PHStat showing relevant statistics and highlight the relevant portions of the output.
- State the null and alternative hypotheses in symbolic form.
- State the type of test and the test statistic you will use.
- What is the critical value of the test statistic?
- What is the value of test statistic for the sample?
- State your decision regarding the null hypothesis.
- State your answer in response to the question "Should the merit raise be given?"