Question

A cognitive psychologist has devised a new paradigm to assess empathy in humans by exposing them to images of other humans in pain and seeing whether this evokes an emotional response in the participants. Among the various aspects of an emotional response is a physiological response, such as variations in normal resting heartrate. It would lend validity to the psychologist's paradigm if exposure to these painful Images causes changes in an individual's normal heartrate. As such, the psychologist selects a random sample of n - 10 male undergraduate Psychology students from an overall pool of eligible students. Each participant is exposed to a painful image for 5 seconds and their Heartrate in beats per minute (BPM) is recorded immediately after. The psychologist reports that the average Heartrate (BPM) of the sample was M = 90 beats per minute. Suppose is known that the normal resting heartrate of this population is u = 70 beats per minute. The distribution of beats per minute is normal with a standard deviation of a 20. Based on the above information, answer the following questions below: QUESTION: Determine the critical region for this test of a(alpha) .01 Please type either directional or non-directional in the blank below. Please remove the quotations for your answert According to the researchers hypothesis, this is a hypothesis test. Please type a number founded to the nearest HUNDREDTHS place (6.8.2.97) as your answer for the blank below Please include either or both / signs before each value as you value for the blank below 6.8.1/2.971 The value of the critical region of this hypothesis test is

Answer 1

are check an nemal As we intrested the exposure to painful images Causes changes individual's hearteate, so we are looking for both lomer and higher heartrate. Thers, its non- directional hypothesis fest. Nall Hypothesis to: ll= 70 H. ll + 70 Significance level As population Standard deviation known, so z-Statistic. Alternate Hypothesis x=0.01 - ce Can use So Critical test statistic - ZA 20.oos +/- 2.58 10 Sample size = Sample mean Population mean 7= 90 - M ll = = 70 differente: M-4 = 90-70 = 120 Population standard deviation = 65 20 Standard Essor = 319 20 1 6.32

Then test statistic is -

M- 20 Z = 3.16 6.32 'n

Thus, Z-statistic for test = 3.16

As the calculated valuel is greater than the critical value of test statiistic, so we reject the null hypothesis and conclude that there is enough evidence in the data to support the claim that the heartrate changes significantly from normal heartrate when people are exposed to painful images of other people.

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Note that in the last part, there seems to be a typo as the question is asking for t-statistic whereas it should be z-statistic. As population standard deviation is known. so you can use a z-test.