(Upload the picture of your solutions. Follow the steps in Test of Hypothesis including your conclusion and round off the critical value and test statistic into 4 decimal places)
STEPS:
- Formulate a null hypothesis (Ho) and the alternative hypothesis (H ).
- Set the level of significance.
- Identify the type of statistical test as either one tailed or two tailed test.
- Determine the tabular value for the test. (Z, t, Chi-square, f)
- Compute for the required statistical test value.
PROBLEM: Amstat News (December 2004) lists median salaries for associate professors of statistics at research institutions and at liberal arts and other institutions in the United States. Assume a sample of 200 associate professors from research institutions having an average salary of $70,750 per year with a standard deviation of $6000. Assume also a sample of 200 associate professors from other types of institutions having an average salary of $65,200 with a standard deviation of $5000. Test the hypothesis that the mean salary for associate professors in research institutions is $2000 higher than for those in other institutions. Use a 0.05 level of significance.
Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.
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