6. A standard drug is used to treat a certain disease. The probability with which the drug is effective is 0.85. A new drug is developed and it is desired to determine if the new drug performs better than the standard. An experiment was conducted with which 300 people are given the new drug.

a. State symbolically the null and alternative hypotheses.

b. What is the critical value and rejection region of the proposed test?

c. If in fact, the success rate of the drug is 0.9, what is the power of the test?

d. When the experiment was actually carried out, it was found that the new drug was effective in 269 of the patients. Find the p-value of the test.

6. A standard drug is used to treat a certain disease. The probability with which the drug is effective is 0.85. A new drug is developed and it is desired to determine if the new drug performs better than the standard. An experiment was conducted with which 300 people are given the new drug.

a. State symbolically the null and alternative hypotheses.

b. What is the critical value and rejection region of the proposed test?

c. If in fact, the success rate of the drug is 0.9, what is the power of the test?

d. When the experiment was actually carried out, it was found that the new drug was effective in 269 of the patients. Find the p-value of the test.

1.A Five hours after the start of an experiment, there were 700 bacteria, and 4 hours after that there were 1200 bacteria. Write a formula for N, the number of bacteria t hours after the start of the experiment, assuming that N is an exponential function.

1.B Let g(x) = 500e.^.06x.Write the inverse of g and specify its domain.

1C. For an investment to double in 20 years, what is the percentage rate of growth(to the nearest percent) necessary? ] Use P = e^rt

1.D. An isotope has a half-life of 7 hours, how much will be left after one day?

During a hiking trip in northern Minnesota, you pull out your pocket microscope and notice that one lake with high acidity levels has a high abundance of water fleas (Daphnia) and a low abundance of a species of zooplankton predator, while another lake with low acidity has few water fleas and many of the predator. You note that Minnesota has many lakes with different acidity levels. You hypothesize that zooplankton do worse in high acidity, allowing Daphnia to flourish. Design tests of this hypothesis using 1) an experimental manipulation, 2) a natural experiment, and 3) a microcosm experiment.

1. In a simple experiment, you are going out there to the duck pond to seine out one redbreast sunfish at random, determine its sex, and put it back in the pond and then, after 30 minutes, repeat this process. Assuming that the sex ratio for redbreast in the pond is 1:1, develop and plot the pmf of the random variable X, defined as the number of females in the two fish observed.
2. 1. Is the distribution of X symmetric or asymmetric?
   2. Explain why the result in (a) was obtained.
   3. Describe a simple experiment (at most 2-3 sentences) that you would perform to determine whether the sex ratio is really 1:1.

We may determine the corresponding equilibrium constant by evaporating acetic acid in a container that is subsequently sealed and weighed. In one experiment, acetic acid was evaporated in a container of volume 21.45 cm3 at 437 K. The pressure of the vapor was 101.9 kPa. The mass of acid in the sealed container was 0.0519 g. The experiment was repeated with the same container (same volume and pressure) at a temperature of 471 K; the mass of acid in the second container was 0.0380 g.

Compute the equilibrium constant for dimerization at each of these temperatures.

Determine the standard reaction enthalpy for this process.

Determine ΔG° and ΔS° for the dimerization reaction at 437 K.

A study involving 5 patients showed that 40% of the population has type O+ blood. Assume that the study maybe modeled by a probability experiment. Let x random variable that represents the possible number of patients that have type O+.

A. In words describe the success and failure for this experiment.

Success=

Failure=

B. What is the probability that exactly 2 patients will have type O+ blood?

C. What is the probability that none of the patients will have type O+ blood?

D. what is the probability that fewer than 3 patients will have type O+ blood?

E. Find the mean, variance, and standard deviation.

In March last year, Goldman Sachs relaxed its dress code, allowing its bankers to swap their bespoke suits for a more casual look. As the CEO of a large financial services company in South Africa, you wonder whether relaxing your existing dress code will result in an improvement in employee morale. To answer your question, you would like to conduct an experiment. Write an essay in which you discuss how you would go about conducting the experiment.

Structure you essay using the following headings:  Design  Participants  Procedure Maximum 600 words.

The experiment is about whether the concentration of sodium bicarbonate will have an effect or not on the rate of photosynthesis in spinach by recording the time taken by the leaf disks to float in the sodium bicarbonate solution with different concentrations (0.7% and 1.5%) as treatment groups and the distilled water as the control group.

Is it possible for leaf disks to float in thecontrol group (Distilled water)?

Why do you think the leaf disks floated at different times in your trial run?

What are the potential sources of error? How will you troubleshoot these when running your experiment?

On what basis will you determine the number of replicates to be used?