2. Does resting membrane potential and equilibrium potential of sodium both change during an action potential?

3. How is the action potential affected with a defect in the Na+/K+ pump and a deleterious mutation in the leak channels?

a) In the first trading day of 1998, Hang Seng Index closed at 10680.60, while in the last trading day of 2017, it closed at 29919.15. What is the average annual growth rate of Hang Seng Index in this 20-year?                              

b) The following yield curve is observed of the U.S. Treasury securities on 28th October 2019:

Suppose the pure expectation theory is correct. Forecast the expected one-year yield rate of one year later and of two years later respectively.  

The Solow Model was originally conceived for a single-good, closed economy. In the ensuing decades, it has been expanded to account for endogenous growth and free trade. We want to consider what kinds of phenomena such models should encompass. Imagine a small developing country initially with a closed economy, with income per capita well below that of advanced nations. The policymakers in this country are considering opening the country to trade. Consider this country’s initial steady state and growth, and discuss how these might change were the country to allow free trade. In particular, focus your response on

1. What would the closed economy steady-state income be relative to advanced nations (and what may cause it to differ)? What about consumption?

2. Would you expect an accelerated speed of growth (capital accumulation) under free trade as compared to a close economy or not? Why yes or why no? What about changes in consumption?

3. What new opportunities for growth may be created by free trade?

Consider the unity feedback negative system with an open-loop function G(s)= K (s^2+10s+24)/(s^2+3s+2).

a. Plot the locations of open-loop poles with X and zeros with O on an s-plane.

b. Find the number of segments in the root locus diagram based on the number of poles and zeros.

c. The breakaway point (the point at which the two real poles meet and diverge to become complex conjugates) occurs when K = 0.02276. Show that the closed-loop system has repeated poles for this K.

d. The break-in point (the point at which the complex conjugate poles meet and diverge to become real) occurs when K = 10.97. Show that the closed-loop system has repeated poles for this K.

e. Find the poles of the closed-loop system when K = 6.

f. Sketch the two segments of the root locus.

g. Check your work using MATLAB. It is not necessary to submit the output.

A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels​ (in milligrams per deciliter of​ blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and​ dependent, and the population is normally distributed. At

can you conclude that the new cereal lowers total blood cholesterol​ levels?

Before   After
two hundred    194
220   216
230   234
245   244
240   236
265   260
225   221

Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative​ hypotheses, where

mu Subscript dμdequals=mu 1 minus mu 2μ1−μ2.

Calculate the standardized test statistic.

t=____

round to 3 decimal places if needed

Calculate the​ P-value.

p-value=___

round to 4 decimal places if it is needed

state the conclusion:

(Reject/fail to reject) H0. There (is/is not) sufficient evidence* to support the claim that the new cereal lowers total

blood cholesterol levels.

.16*

The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in high-crime areas of Miami, Florida, are being examined to test the effectiveness of the program. The difference in crimes reported is calculated as (crimes after - crimes before). You want to test whether the crimes reported before is greater than those reported after and, thus, the hypotheses are as follows: Null Hypothesis: ?D ? 0, Alternative Hypothesis: ?D > 0. You perform a paired sample t-test and see a p-value of 0.0487. What is the appropriate conclusion?

Question 9 options:

1) The average difference in crimes reported is significantly different from 0. There is a significant difference in crimes reported due to the program.

2) The average difference in crimes reported is significantly less than 0. The average number of crimes reported was higher before the program.

3) The average difference in crimes reported is less than or equal to 0.

4) The average difference in crimes reported is significantly larger than 0. The average number of crimes reported was higher after the program.

5) We did not find enough evidence to say there was a significantly positive average difference in crimes reported. The program does not appear to have been effective.

Drunk driving is one of the main causes of car accidents. Interviews with drunk drivers who were involved in accidents and survived revealed that one of the main problems is that drivers do not realise that they are impaired, thinking “I only had 1-2 drinks … I am OK to drive.” A sample of 5 drivers was chosen, and their reaction times (seconds) in an obstacle course were measured before and after drinking two beers. The purpose of this study was to check whether drivers are impaired after drinking two beers. Below is the data gathered from this study:

Driver 1 2 3 4 5

Before 6.15 2.86 4.55 3.94 4.19

After 6.85 4.78 5.57 4.01 5.72. (a)The two measurements are dependent. Explain? why?

(b)Provide an estimate of the mean difference in reaction times between the two measurements? (c)Calculate and interpret a 95% confidence interval for the mean difference in reaction times between the two measurements?

(d)Use a 5% level of significance and the following points to test the claim that reaction times before drinking two bears is lower than reaction times after drinking two bears.

(i) State the null and alternative hypotheses in symbolic form and in context.

(ii) Calculate the test statistic.

(iii) Identify the rejection region(s).

(iv) Clearly state your conclusions (in context). (e)What would the conclusion be if using a 1% level of significance? Justify your answer

II-(7 pts) A city wants to know if a new advertising campaign to make citizens aware of the dangers of

driving after drinking has been effective. They count the number of drivers who have been stopped with

more alcohol in their systems than the law allows for each day of the week in the week before and the

week a month after the campaign starts. Let ?? be the difference between the number of drivers caught

with excessive alcohol in their systems before and after the campaign on each calendar day in any given

week. Treat these as a random sample from a Normal (?, ??) distribution.

Information collected randomly during the seven days of a week before and a week a month after the

campaign, indicate a mean difference ?̅ = −2 , and a standard deviation ? = 3.162.

a. Obtain a 95% confidence interval for the true average difference in number of drivers stopped with

excess alcohol in their systems. (1pt)

b. You are asked by the city administration to study whether the advertising campaign has been

effective. State in terms of , the relevant null and alternative hypothesis in conducting this study. (1pt)

c. Compute the t statistic for testing ?? against ?? (1pt)

d. Obtain the p- value for the test (1pt)

e. Do you reject ?? at the 5% level? At the 1% level? (1pt)

f. Provide a short summary of your conclusions from this study. Comment on the practical versus

statistical significance of this estimate. (2pts)

w

1 w

b R b R

b R w

1 w s b R  wR  (1 w)R



A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are asked again to give their most recent score. The scores for each golfer are given in the table below. Is there enough evidence to support the manufacturer's claim? Let d=(golf score after using the newly designed golf clubs)−(golf score before using the newly designed golf clubs) d = (golf score after using the newly designed golf clubs) − (golf score before using the newly designed golf clubs) . Use a significance level of α=0.05 α = 0.05 for the test. Assume that the scores are normally distributed for the population of golfers both before and after using the newly designed clubs. Golfer 1 2 3 4 5 6 7 8 Score (old design) 76 76 91 91 76 76 77 77 83 83 94 94 88 88 83 83 Score (new design) 72 72 92 92 75 75 72 72 89 89 88 88 82 82 78 78 Copy Data Step 3 of 5 : Compute the value of the test statistic? Round your answer to three decimal places.

What is the P-value? Reject or Fail?