In a study of hypnotic suggestion, 16 male volunteers were randomly allocated to a treatment group and a control group. Each subject participated in a two-phase experimental session. In the first phase, respiration was measured while the subject was awake and at rest. In the second phase, the subject was told to imagine that he was performing muscular work, and respiration was measured again. For subjects in the treatment group, hypnosis was induced between the first and second phases; thus, the suggestion to imagine muscular work was "hypnotic suggestion" for treatment subjects and "waking suggestion" for control subjects. The table below shows the measurements of total ventilation (liters of air per minute per square meter of body area) for all 16 subjects. Treatment Group Control Group Total Ventilation Difference Total Ventilation Difference Subject Rest Work Subject Rest Work (Work-Rest) (Work-Rest) 0.50 1 5.74 6.24 9 6.21 5.50 -0.71 6.79 9.07 2.28 10 4.50 4.64 0.14 3 5.32 7.77 2.45 11 4.86 4.61 -0.25 4 7.18 16.46 9.28 12 4.78 3.78 -1.00 5 5.60 6.95 1.35 13 4.79 5.41 0.62 6. 6.06 8.14 2.08 14 5.70 5.32 -0.38 7 6.32 11.72 5.40 15 5.41 4.54 -0.87 8 6.34 8.06 1.72 16 6.08 5.98 -0.10 Mean 6.16875 9.30125 3.1325 Mean 5.29125 4.9725 -0.31875 SD 0.62109 3.32276 2.8620 SD 0.65160 0.7027 0.54368 For those being hypnotized (treatment group), test the hypotheses Ho: Hrest = Hwork versus Ha: Hrest # Hwork, where µrest and Hwork are respectively the mean total ventilation when they are at rest and when they are performing imaginary muscular work. Please report the test statistic with degrees of freedom, and (a range for) the P-value. What do you conclude at 0.05 significance level? Construct a 95% confidence interval for the mean difference Hwork - Hrest in their total ventilation when the subjects are at rest and when performing imaginary muscular work if hypnosis is induced between the two phases. Check your computation in (a) and (b) with the R commands below. Rest = c(5.74,6.79,5.32,7.18,5.60,6.06,6.32,6.34) Work = c(6.24,9.07,7.77,16.46,6.95,8.14,11.72,8.06) t.test (Work, Rest, paired = T) Check the plot(s) for the data in the treatment group. Do you see any outlier or severe skewness that make you concern about appropriateness of conducting the test and constructing the confidence interval in part (a) and (b)? Test whether hypnosis (treatment) induced a greater change in in total ventilation than no hypnosis (control). That is, test the hypotheses Họ: Htrt, work - Htrt, rest = Hetrl,work - Hetrl,rest Ha : Ptrt, work - Htrt, rest > Hetrl,work - Hctrl,rest where Hert, work-Htrt, rest is the mean change in total ventilation at work v.s. at rest for the hypnotized (treatment) group, and Hetri,work - Hctrl,rest is the corresponding change for the control group. Please report the test statistic with degrees of freedom, and give (a range for) the P-value. Did hypnosis induce a significantly higher change in total ventilation at 0.05 level? Hint: Should you conduct a two-sample t-test or a paired t-test?

In a study of hypnotic suggestion, 16 male volunteers were randomly allocated to a treatment group and a control group. Each subject participated in a two-phase experimental session. In the first phase, respiration was measured while the subject was awake and at rest. In the second phase, the subject was told to imagine that he was performing muscular work, and respiration was measured again. For subjects in the treatment group, hypnosis was induced between the first and second phases; thus, the suggestion to imagine muscular work was "hypnotic suggestion" for treatment subjects and "waking suggestion" for control subjects. The table below shows the measurements of total ventilation (liters of air per minute per square meter of body area) for all 16 subjects. Treatment Group Control Group Total Ventilation Difference Total Ventilation Difference Subject Rest Work Subject Rest Work (Work-Rest) (Work-Rest) 0.50 1 5.74 6.24 9 6.21 5.50 -0.71 6.79 9.07 2.28 10 4.50 4.64 0.14 3 5.32 7.77 2.45 11 4.86 4.61 -0.25 4 7.18 16.46 9.28 12 4.78 3.78 -1.00 5 5.60 6.95 1.35 13 4.79 5.41 0.62 6. 6.06 8.14 2.08 14 5.70 5.32 -0.38 7 6.32 11.72 5.40 15 5.41 4.54 -0.87 8 6.34 8.06 1.72 16 6.08 5.98 -0.10 Mean 6.16875 9.30125 3.1325 Mean 5.29125 4.9725 -0.31875 SD 0.62109 3.32276 2.8620 SD 0.65160 0.7027 0.54368 For those being hypnotized (treatment group), test the hypotheses Ho: Hrest = Hwork versus Ha: Hrest # Hwork, where µrest and Hwork are respectively the mean total ventilation when they are at rest and when they are performing imaginary muscular work. Please report the test statistic with degrees of freedom, and (a range for) the P-value. What do you conclude at 0.05 significance level? Construct a 95% confidence interval for the mean difference Hwork - Hrest in their total ventilation when the subjects are at rest and when performing imaginary muscular work if hypnosis is induced between the two phases. Check your computation in (a) and (b) with the R commands below. Rest = c(5.74,6.79,5.32,7.18,5.60,6.06,6.32,6.34) Work = c(6.24,9.07,7.77,16.46,6.95,8.14,11.72,8.06) t.test (Work, Rest, paired = T) Check the plot(s) for the data in the treatment group. Do you see any outlier or severe skewness that make you concern about appropriateness of conducting the test and constructing the confidence interval in part (a) and (b)? Test whether hypnosis (treatment) induced a greater change in in total ventilation than no hypnosis (control). That is, test the hypotheses Họ: Htrt, work - Htrt, rest = Hetrl,work - Hetrl,rest Ha : Ptrt, work - Htrt, rest > Hetrl,work - Hctrl,rest where Hert, work-Htrt, rest is the mean change in total ventilation at work v.s. at rest for the hypnotized (treatment) group, and Hetri,work - Hctrl,rest is the corresponding change for the control group. Please report the test statistic with degrees of freedom, and give (a range for) the P-value. Did hypnosis induce a significantly higher change in total ventilation at 0.05 level? Hint: Should you conduct a two-sample t-test or a paired t-test?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...

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