A)

A researcher was interested in the short-term effect that caffeine has on heart rate. He enlisted a group of 105 volunteers and measured each person's resting heart rate. Then he had each subject drink six ounces of coffee. 34 of the subjects were given coffee containing caffeine and F1 were given decaffeinated [decaf] coffee. After 10 minitues each person's heart rate was measured again. For volunteers who had coffee containing caffeine, the mean difference of their hear rate was found to he 13?. and for the volunteers who took decaffeinated coffee had a mean difference of heart rate as 5.02. Moreover, the sample standard deviations were 3.?3 for caffeine group and 3.23 for decaf group. The researcher who conducted this studv has decided to perform a hypothesis test to check whether the population means for the difference of heart rates in these two groups are equal or not. 1Fill-"hat degrees of freedom should he use for his reference t-distrihution? Let u be the true mean hours studied by students for the final exam. It has been provided that a good estimate of standard deviation (s*) is 20 hours. What is the minimum sample size of n needed to achieve a margin of error (m) less than 5 hours? You may assume that, when n=58, t* = 2.0025 when n=63, t* = 1.999 when n=64, t*= 1.9983 when n=69, t* = 1.9955 63 O 64 O 69 O 58Which of the following statements are true about type I error, type II error and power of a test? You may choose more than one answers. O) If the significance level is 0.05 we might make a type | error 95% of the time. O A researcher might reject HO, when it was false. This is an example of Type | error. O A researcher might fail to reject HO even though it was false. This is an example of Type II error. O If the probability of type II error is 0.14 then the power of the test is 0.86. O) For a fixed sample size, when the probability of type I error gets smaller, probability of type II error gets larger