Question

a journalist is interested in whether there is a significant difference in the salary offered to electrical engineering and chemical engineering graduates at the university of texas at austin. she reviews the statistics for starting annual salaries for 2013 - 2014 and finds the following: the test statistic is ( t = 2.4693 ), with a p - value of 0.0142. which of the following is an appropriate conclusion? a. the samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the university of texas at austin for 2013 - 2014. b. the samples do not provide statistically significant evidence that there is a difference in starting salaries of chemical engineering and electrical engineering graduates at the university of texas at austin for 2013 - 2014. c. we cannot use the t - test in this case because the variables (starting salary of engineering graduates) may not be normally distributed.

Explanation:

• In hypothesis testing, if the p - value is less than the significance level (commonly \(\alpha = 0.05\)), we reject the null hypothesis.
• Here, the p - value is \(0.0142\) which is less than \(0.05\).
• Rejecting the null hypothesis implies that there is a statistically significant difference.
• For option C, the Central Limit Theorem states that for large sample sizes (\(n_1=91\) and \(n_2 = 160\)), the sampling distribution of the sample mean is approximately normal even if the population is not normal. So, the t - test is valid.

Answer:

A. The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013 - 2014.