High blood pressure (hypertension) is a leading cause of strokes. Medical researchers are constantly seeking ways to treat patients suffering from this condition. A specialist in hypertension claims that regular aerobic exercise can reduce high blood pressure just as successfully as drugs, with none of the adverse side effects. To test the claim, 50 patients who suffer from high blood pressure were chosen to participate in an experiment. For 60days, half the sample exercised three times per week for 1 hour and did not take medication; the other half took the standard medication. The percentage reduction in blood pressure was recorded for each individual. Estimate with 95% confidence the difference in mean percentage reduction in blood pressure between drugs and exercise programs.

A researcher wants to test the effectiveness of a new medication designed to lower blood pressure. Identify a potential problem, if any, with the experimental design. Then describe how you can improve it. The researcher identifies 30 people with high blood pressure. Fifteen people with the highest blood pressures are given the medication and the other 15 are given a placebo. After 1 month, the subjects are evaluated.

People found to have high blood pressure are started on a course of tablets and have their blood pressure checked at the end of 4 weeks. The drop in blood pressure over the period is normally distributed with mean 5.9 units and standard deviation 1.9 units. Find the proportion of people who show a drop of more than 4 units.

The article “Dynamics of Insulin Action in Hypertension: Assessment from Minimal Model Interpretation of Intravenous Glucose Tolerance Test Data” compared levels of an insulin sensitivity index $S_I$ in patients with high blood pressure and patients with normal blood pressure. Ten patients with high blood pressure had a mean value of 3.4 with a standard deviation of 0.6, and eight patients with normal blood pressure had a mean value of 7.9 with a standard deviation of 0.6. Units are $10^{−5} \cdot min^{−1} \cdot pmol^{−1}.$ Find a 98% confidence interval for the difference in mean levels between those with high blood pressure and those with normal blood pressure.

The gusset plate shown is subjected to four concurrent forces. If $F_1=150\ \mathrm{lb}, F_2=240\ \mathrm{lb}, F_3=180\ \mathrm{lb}$, and $F_4=$ $300\ \mathrm{lb}$, determine the magnitude and direction of the resultant graphically by the polygon method.

Jim's systolic blood pressure is a random variable with a mean of $145 \mathrm{mmHg}$ and a standard deviation of $20 \mathrm{mmHg}$. For Jim's age group, 140 is the cutoff for high blood pressure. (a) If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 135 or less? (b) 175 or more? (c) Between 125 and 165? (d) Discuss the implications of variability for physicians who are trying to identify patients with high blood pressure.

A U.S. pharmaceutical company is considering manufacturing and marketing a pill that will help to lower both an individual's blood pressure and cholesterol. The company is interested in understanding the demand for such a product. The joint probabilities that an adult American man has high blood pressure and/or high cholesterol are displayed in the table.

$$\begin{array}{lcc} & \text { High } & \text { OK } \\ \text { High } & 0.11 & 0.21 \\ \text { OK } & 0.16 & 0.52\end{array}$$

a) What's the chance that an adult American male has both conditions?

The blood pressure in a person’s feet is greater that the pressure in his head. Estimate this pressure difference and compare it with normal blood pressure.

Consider a thin homogeneous plate that lies in the $x_{1}-x_{2}$ plane. Show that the inertia tensor takes the form

$$\{\mathbf{I}\}=\left\{\begin{array}{rrr} A & -C & 0 \\ -C & B & 0 \\ 0 & 0 & A+B \end{array}\right\}$$

Two infinite parallel grounded conducting planes are held a distance a apart. A point charge q is placed in the region between them, a distance x from one plate. Find the force on q. Check that your answer is correct for the special cases $a\rightarrow\infty$ and $x=a/2$.

A study of the effects of exercise used rats bred to have high or low capacity for exercise. The 8 high-capacity rats had mean blood pressure 89 and standard deviation 9; the 8 low-capacity rats had mean blood pressure 105 with standard deviation 13. (Blood pressure is measured in millimeters of mercury.)

The two-sample t statistic for comparing the two population means has value

(a) 0.5.

(b) 2.86.

(c) 9.65.

A parallel-plate, air-filled capacitor is being charged as in Fig. we saw earlier. The circular plates have radius $4.00 \mathrm{~cm}$, and at a particular instant the conduction current in the wires is $0.520 \mathrm{~A}$. At $1.00 \mathrm{~cm}$ from the axis?

Two baseballs are pitched horizontally from the same height, but at different speeds. The faster ball crosses home plate within the strike zone, but the slower ball is below the batter’s knees. Why does the faster ball not fall as far as the slower one?

One study discussed a pilot study of people who suffer from abnormally high blood pressure. A medical researcher decides to test her belief that walking briskly for at least half an hour a day has the effect of lowering blood pressure. She randomly samples three of her patients who have high blood pressure. She measures their systolic blood pressure initially and then again a month later after they participate in her exercise program. The table shows the results. Show how to analyze the data with the sign test. State the hypotheses, find the P-value, and interpret.