It is required to determine whether the Yellow or White University has more adva

Question

It is required to determine whether the Yellow or White University has more advanced program for engineering. It is suggested that if the average of income for newly graduated undergraduates is significantly higher for one of these universities, this indicates that the marketplace values the graduates of that university more highly, which suggests that the education program of that university is of higher quality.

Yellow: $55,000; $65,000; $45,000; $85,000; $45,000; $70,000; $60,000; $50,000; $100,000; $50,000; $75,000; $85,000; $70,000; $80,000

White: $60,000; $80,000; $50,000; $75,000; $50,000; $60,000; $75,000; $45,000; $50,000; $65,000; $60,000; $65,000; $50,000

Assume the salaries for graduates of both institutions are normally distributed, and that there is no dependence between the samples drawn from the two populations. Assume the variances of the salaries are known and equal to $225,000,000 dollars2.

(a) Develop and test the hypothesis that the average starting salary for Yellow graduates is higher than that for White graduates. Assume that the level of significance is .05.

(b) Given the data calculated in part (a), then if the variance of the salary data is the same for both institutions, what must be true about that variance to ensure that the null hypothesis in part (a) would be rejected at the .01 significance level?

(c) Repeat part (a) under the condition that the variances of the salaries are unknown, and that these unknown variances are equal. What is the p-value?

(d) Repeat part (a) under the condition that the variances are unknown, and that these unknown variances should not be assumed to be equal.

(e) Develop and test a (an?) hypothesis concerning whether the variances are equal, or whether the population with the larger sample variance actually has the larger variance. Assume the level of significance is .05. What is the p-value?

Explanation / Answer

a) Yellow: 55000, 65000, 45000, 85000, 45000, 70000, 60000, 50000, 100000, 50000, 75000, 85000, 70000, 80000

Mean:66785.714285714

Variance (2): 266454081.63265

The T-value is 0. The P-Value is 1. The result is not significant at p < 0.05.

White: 60000, 80000, 50000, 75000, 50000, 60000, 75000, 45000, 50000, 65000, 60000, 65000, 50000

Mean: 60384.61538

Variance (2): 117159763.31361

The T-value is 0. The P-Value is 1. The result is not significant at p < 0.05.

The average starting salary for both Yellow graduates and White graduates are same.

b) Null Hypothesis and variance :

Yellow:The T-value is 0. The P-Value is 1. The result is not significant at p < 0.01.

Variance (2): 266454081.63265

White: The T-value is 0. The P-Value is 1. The result is not significant at p < 0.01

Variance (2): 117159763.31361

c) P-value = 1

Mean: 60384.61538

Variance (2): 117159763.31361

The T-value is 0. The P-Value is 1. The result is not significant at p < 0.05.

The average starting salary for both Yellow graduates and White graduates are same.

b) Null Hypothesis and variance :

Yellow:The T-value is 0. The P-Value is 1. The result is not significant at p < 0.01.

Variance (2): 266454081.63265

White: The T-value is 0. The P-Value is 1. The result is not significant at p < 0.01

Variance (2): 117159763.31361

c) P-value = 1

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