6.30. Studies have considered whether neonatal sex differences exist in behavioral and physiological reactionsto stress. One study6 evaluated changesin heart rate for a sample ofinfants placed in a stressfulsituation. The sample mean change in heart rate was small for males compared to females: —1.2 compared to 10.7, each with standard deviations of about 18. Suppose we arc skeptical ofthe result for males and plan a larger experiment to test whether the mean heart rate increases when male infants undergo the stressful experience. Let /x denote the population mean of the difference in heart rates, after versus before the stress. We'll test Ho'- /r = 0 against Ha: /x > 0, at the a = 0.05 level using n - 30 infant males. Suppose the standard deviation is 18. Find P(Typc II error) if/x = 10 by showing

(a) a test statistic of t = 1.699 has a P-value of 0.05,

(b) we failto reject Ho ify < 5.6,

(c) this happens ify falls more than 1.33 standard errors below 10,

(d) this happens with probability about 0.10.