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(14 For each question below, set up the null and alternative hypotheses, calculate the test statistic, nd and draw the rejection region for the test and state the appropriate conclusion. a] The mean SAT math reasoning score in EH10 was 515, with a standard deviation of 114. An educational psychologist believes that students who take at least 4 years of English courses in high school score better on the SAT math reasoning exam. The psychologist obtains a random sample of 41\".] high school students who completed at least 4 years of English courses in high school and finds that their mean SAT math reasoning exam score is 544]. Illustrate an appropriate test at the alpha is 0.05 level of signicance to determine if the psychologist's belief is supported by the data. [10 marks] b] Laughter is often called 'the best medicine' since studies have shown that laughter can reduce muscle tension and increase oxygen in blood, 90 subjects [1834 yea rs old] watched film clips designed to evoke laughter. During the laughing period, the researchers measured the heart rate {beats per minute] of each subject, with the following results: ; = 3'35, s = 6. It is well known that the mean resting heart rate of adults is ?1 beats per minute. Setup hypothesis testing whether the true mean heart rate during laughter exceeds 3'1 beats per minute. Illustrate an appropriate test at the alpha 0.05 level of signicance. [It] marks] c] Do business travellers walk at a different pace than leisure travellers? Researcher measured the walking speed of business and leisure travellers in Kuala Lumpur International Airport. His findings are summarized in Table 4 below. Illustrate an appropriate test at the alpha {1115 level of significance. m Traveller Mean speed (feet per minute] 261 Standard deviation {feet per minute] Sample size [11\".]I marks]