A student to decide whether he wants to major in electrical or mechanical engine
ID: 3155955 • Letter: A
Question
A student to decide whether he wants to major in electrical or mechanical engineering or computer science. To find out which job pays more, he interviews eight alumni in each profession and asks them what their starting salary was. The electrical engineering alumni had a mean starting salary of $54,000 and a standard deviation of $8,000. The computer science alumni had a mean starting salary $62,000 and a standard deviation of $10,000. It is reasonable to assume equal population variances, and assume starting salaries are normally distributed. Specify the competing hypothesis to determine if electrical engineering and computer science majors mean starting salaries are equal. Calculate the value of the test statistic, and find the critical value at a 5 % significance level. Make a conclusion at the 5% significance level.Explanation / Answer
A)
Let u1 = electrical engineering mean starting salary
u2 = computer science mean starting salary
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0 [ANSWER]
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b)
Calculating the means of each group,
X1 = 54000
X2 = 62000
Calculating the standard deviations of each group,
s1 = 8000
s2 = 10000
Thus, the pooled standard deviation is given by
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]
As n1 = 8 , n2 = 8
Then
S = 9055.385138
Thus, the standard error of the difference is
Sd = S sqrt (1/n1 + 1/n2) = 4527.692569
As ud = the hypothesized difference between means = 0 , then
t = [X1 - X2 - ud]/Sd = -1.766904417 [ANSWER, TEST STATISTIC]
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At level of significance = 0.05
As we can see, this is a two tailed test.
Getting the critical value using table/technology,
df = n1 + n2 - 2 = 14
tcrit = +/- 2.144786688 [ANSWER, CRITICAL VALUES]
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c)
As |t| < 2.145, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that the starting salaries for electrical engineering and computer science are different at 0.05 level. [CONCLUSION]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!
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