The probability that a medical treatment is effective is 0.68, unknown to a researcher. In an experiment to investigate the effectiveness of the treatment, the researcher applies the treatment in 140 cases and measures whether the treatment is effective or not. What is the probability that the researcher’s estimate of the probability that the medical treatment is effective is within 0.05 of the correct answer?

A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?

What was Pavlov conducting research on before he started researching associations?

Developing a new drug can be an expensive process, resulting in high costs to patients. A pharmaceutical company has developed a new drug to reduce cholesterol, and it will conduct a clinical trial to compare the effectiveness to the most widely used current treatment. The results will be analyzed using a hypothesis test.

If the test yields a high P-value and the researcher fails to reject the null hypothesis, but the new drug is more effective, what are the consequences of such an error?

A medical researcher wishes to estimate the percentage of females who take vitamins. He wishes to be 98% confident that the estimate is within 4 percentage points of the true proportion. What is the minimum sample size needed?

State the null hypothesis, $H_0$, and the alternative hypothesis, $H_a$, to be tested. A researcher claims that a binomial proportion $p$ is at least $0.8$. A statistical test is designed to disprove the researcher's claim.

Write the Lewis structure for each ion. Include resonance structures if necessary and assign formal charges to all atoms. If necessary, expand the octet on the central atom to lower formal charge. a. $PO_4^{3-}$ b . $CN^-$ c. $SO_3 ^{2-}$ d. $ClO_2 ^-$

Deduce from part (a) of the preceding exercise that $\frac{d}{d t} \exp (A t)=A \exp (A t)$ Now let $y_{1}(t), \ldots, y_{n}(t)$ be differentiable functions of the real variable $t$ that are related by the following linear system of first order differential equations with constant coefficients $a_{i j} \in K$

$$y_{1}^{\prime}=a_{11} y_{1}+a_{12} y_{2}+\ldots+a_{1 n} y_{n}$$

$$y_{2}^{\prime}=a_{21} y_{1}+a_{22} y_{2}+\ldots+a_{2 n} y_{n}$$

$$y_{n}^{\prime}=a_{n 1} y_{1}+a_{n 2} y_{2}+\ldots+a_{n n} y_{n}$$

(here the primes denote derivatives with respect to $t$ ). Let $A$ be the matrix whose $i, j$ entry is $a_{i j},$ so that $(*)$ may be written as

$$\left( \begin{array}{c}{y_{1}^{\prime}} \\ {y_{2}^{\prime}} \\ {\vdots} \\ {y_{n}^{\prime}}\end{array}\right)=A \left( \begin{array}{c}{y_{1}} \\ {y_{2}} \\ {\vdots} \\ {y_{n}}\end{array}\right)$$

or, more succinctly, as $y^{\prime}=A y,$ where $y$ is the column vector of functions $y_{1}(t), \ldots, y_{n}(t)$ An $n \times n$ matrix whose entries are functions of $t$ and whose columns are independent solutions to the system $(*)$ is called a fundamental matrix of $(*) .$ By the theory of differential equations, the set of vectors $y$ that are solutions to the system $(*)$ form an $n$ -dimensional vector space over $K$ and so the columns of a fundamental matrix are a basis for the vector space of all solutions to $(*)$

The proton has a radius of approximately $1.0 \times 10^{-13}$ cm and a mass of $1.7 \times 10^{- 24}$ g. Determine the density of a proton for a sphere $V = (4/3) \pi r^3$

Determine whether the description corresponds to an observational study or an experiment:

The researcher wants to determne the difference in the academic performance of accounting students from difference school. Thus, the midterm examination result for the colleges were retrieved by researchers.The result of the test were compared and described by the researchers.

Suppose that a set of observations is collected from a beta distribution, with an average of $\bar{x} = 0.782$ and a variance of $s^2 = 0.0083$. Obtain point estimates of the parameters of the beta distribution.

Suppose that $X \sim B(12, p)$ and consider the point estimate

$$\hat{p} =\dfrac{X}{14}$$

(a) What is the bias of this point estimate? (b) What is the variance of this point estimate? (c) Show that this point estimate has a mean square error of

$$\dfrac{3p − 2p^2}{49}$$

(d) Show that this mean square error is smaller than the mean square error of $X/12$ when $p \le 0.52$.

Increasing the sample size: A. Tends to increase the standard error of the estimates with an increased experimental cost B. Tends to decrease the standard error of the estimates with a decreased experimental cost C. Tends to increase the standard error of the estimates with a decreased experimental cost D. Tends to decrease the standard error of the estimates with an increased experimental cost

Suppose that the spot price of the euro is currently $1.30. The one-year futures price is$1.35. Is the U.S. interest rate higher than the euro rate?