Hypothesis Test: .edu



Hypothesis Test:

The null and alternative hypothesis for this test are:

Ho : mu1 – mu2 = 0

Ha : mu1 – mu2 != 0

We use a two tailed t- test to test the differences of the means between the Masters and phD alumni at a 5% level of significance.

The Table shows the the values computed for this test.

(If the p-value < alpha (.025), then print)

Since the p-value < alpha , we reject the null hypothesis

Conclusion: We do not have enough evidence to conclude that there is no difference between the mean salaries.

(If the p-value > alpha (.025), then print)

Since the p-value > alpha , we fail to reject the null hypothesis

Conclusion: We do not have enough evidence to conclude that there is a difference between the mean salaries.

Chi Square test:

One of the applications of a Chi-square distribution is for testing independence of random variables. For this test, we are testing to check if finding a job within three months of graduation is independent of the alumni’s citizenship at a 0.05 level of significance.

The null and alternative hypotheses are as follows:

Ho: the alumni’s citizenship and his getting a job within three months of graduation are independent

Ha: the alumni’s citizenship and his getting a job within three months of graduation are not independent

The contingency table shows the observed values and the corresponding expected values calculated for the test. There are two rows and two columns so it is a 2 x 2 table.

The degrees of freedom come out to be 1 and hence the critical chi-square value = 3.84.

The chi-sqaure sample statistic comes out to be -----------.

( If the CS sample statistic is larger than the critical CS value , then print….)

Since CS sample statistic is larger than the critical CS value, we reject the null hypothesis of independence.

Conclusion: The alumni’s citizenship and his getting a job within three months of graduation are not independent

OR

( If the CS sample statistic is less than the critical CS value , then print….)

Since CS sample statistic is less than the critical CS value, we fail to reject the null hypothesis of independence.

Conclusion: The alumni’s citizenship and his getting a job within three months of graduation are independent

Simple Linear Regression:

For simple linear Regression we are analyzing the relationship between the GPA of an alumni and the salary he earns based on whether the alumni has a Masters or a Phd degree. Scatter plots for MS and PhD alumni are plotted separately and their statistic is computed.

For our criteria of best-fitting line, we use the least squares criterion. The equation of a line which best fits the sample data is given in terms of y = bx + c where b is the slope of the line and a is the y-intercept.

To measure the spread os a set of points about the least squares line we use the standard error of estimate, coefficient of correlation and the coefficient of determination.

The coefficient of determination, R2 is a measure of the proportion of variation in salary that is explained by the GPA. The rest is due to other factors.

The correlation coefficient is a unit less measure which describes the strength of the linear association between the salary and the Gpa. The std error gives the spread of the sample points in terms of the differences between the experimental and predicted salary values for a given GPA.The sum of squares SS and the mean squares due to error MS measure the variability due to error.

Correlation:

The scatter plot shows the correlation between the GPA of an alumni and the salary he earns. The explanatory variable is the GPA and the response variable is the salary. The correlation coefficient is a unitless measure used to describe the strength of the linear association between the salary and the GPA regardless of which is listed first.

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