How does the scientifi c method differ from each of the methods listed here? a. Method of authority b. Method of rationalism c. Method of intuition

Explain two ways in which DNA replication can introduce doubled-strand breaks (DSBs) in a DNA template.

A. Draw the structure of deoxyguanosine. Circle and label the appropriate hydrogen bond donors (D) or acceptors (A) that participate in hydrogen bonding when a base pair with deox-ycytidine forms in DNA. B. Draw the structure of guanosine. Circle and label the appropriate hydrogen bond donors (D) or acceptors (A) that participate in hydrogen bonding when a base pair with uridine forms in RNA.

Which strategy for differential gene expression do Saccharomyces cerevisiae cells use in the regulation of mating-type switching? Name the relevant mRNA or protein used in the strategy.

A column of 22.5-ft effective length must carry a centric load of 288 kips. Using allowable stress design, select the wide-flange shape of 14-in. nominal depth that should be used. Use $\sigma Y=50$ ksi and $E=29 \times 106$ psi.

The diameter of fuse pins used in an aircraft engine application is an important quality characteristic. Twenty-five samples of three pins each are as follows (in mm).

$$\begin{matrix} \text{Sample Number} & \quad & \text{Diameter} & \quad\\ \text{1} & \text{64.030} & \text{64.002} & \text{64.019}\\ \text{2} & \text{63.995} & \text{63.992} & \text{64.001}\\ \text{3} & \text{63.988} & \text{64.024} & \text{64.021}\\ \text{4} & \text{64.002} & \text{63.996} & \text{63.993}\\ \text{5} & \text{63.992} & \text{64.007} & \text{64.015}\\ \text{6} & \text{64.009} & \text{63.994} & \text{63.997}\\ \text{7} & \text{63.995} & \text{64.006} & \text{63.994}\\ \text{8} & \text{63.985} & \text{64.003} & \text{63.993}\\ \text{9} & \text{64.008} & \text{63.995} & \text{64.009}\\ \text{10} & \text{63.998} & \text{74.000} & \text{63.990}\\ \text{11} & \text{63.994} & \text{63.998} & \text{63.994}\\ \text{12} & \text{64.004} & \text{64.000} & \text{64.007}\\ \text{13} & \text{63.983} & \text{64.002} & \text{63.998}\\ \text{14} & \text{64.006} & \text{63.967} & \text{63.994}\\ \text{15} & \text{64.012} & \text{64.014} & \text{63.998}\\ \text{16} & \text{64.000} & \text{63.984} & \text{64.005}\\ \text{17} & \text{63.994} & \text{64.012} & \text{63.986}\\ \text{18} & \text{64.006} & \text{64.010} & \text{64.018}\\ \text{19} & \text{63.984} & \text{64.002} & \text{64.003}\\ \text{20} & \text{64.000} & \text{64.010} & \text{64.013}\\ \text{21} & \text{63.988} & \text{64.001} & \text{64.009}\\ \text{22} & \text{64.004} & \text{63.999} & \text{63.990}\\ \text{23} & \text{64.010} & \text{63.989} & \text{63.990}\\ \text{24} & \text{64.015} & \text{64.008} & \text{63.993}\\ \text{25} & \text{63.982} & \text{63.984} & \text{63.995}\\ \end{matrix}$$

(a) Set up $\overline{X}$ and R charts for this process. If necessary, revise limits so that no observations are out of control. (b) Estimate the process mean and standard deviation. (c) Suppose the process specifications are at $64 \pm 0.02.$ Calculate an estimate of $C_p.$ Does the process meet a minimum capability level of $C_{p} \geq 1.33 ?$ (d) Calculate an estimate of $C_{pk}.$ Use this ratio to draw conclusions about process capability. (e) To make this process a six-sigma process, the variance $\sigma^{2}$ would have to be decreased such that $C_{pk} =2.0.$ What should this new variance value be? (f ) Suppose the mean shifts to 64.005. What is the probability that this shift will be detected on the next sample? What is the ARL after the shift?

Consider the data and simple linear regression. (a) Find the mean deflection given that the temperature is 74.0 degrees. (b) Compute a 95% CI on this mean response. (c) Compute a 95% PI on a future observation when temperature is equal to 74.0 degrees. (d) What do you notice about the relative size of these two intervals? Which is wider and why? Perform the following. (a) Estimate the intercept $\beta_0$ and slope $\beta_1$ regression coefficients. Write the estimated regression line. (b) Compute the residuals. (c) Compute SSE and estimate the variance. (d) Find the standard error of the slope and intercept coefficients. (e) Show that SST = SSR + SSE. (f) Compute the coefficient of determination, R2. Comment on the value. (g) Use a t-test to test for significance of the intercept and slope coefficients at $\alpha = 0.05.$ Give the P-values of each and comment on your results. (h) Construct the ANOVA table and test for significance of regression using the P-value. Comment on your results and their relationship to your results in part (g). (i) Construct 95% CIs on the intercept and slope. Comment on the relationship of these CIs and your findings in parts (g) and (h). (j) Perform model adequacy checks. Do you believe the model provides an adequate fit? (k) Compute the sample correlation coefficient and test for its significance at $\alpha = 0.05.$ Give the P-value and comment on your results and their relationship to your results in parts (g) and (h). Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection (y). The data follow.

$$\begin{matrix} \text{Temperature x} & \text{Deflection y} & \text{Temperature x} & \text{Deflection y}\\ \text{70.0} & \text{0.621} & \text{72.7} & \text{0.637}\\ \text{77.0} & \text{0.657} & \text{67.8} & \text{0.627}\\ \text{72.1} & \text{0.640} & \text{76.6} & \text{0.652}\\ \text{72.8} & \text{0.623} & \text{73.4} & \text{0.630}\\ \text{78.3} & \text{0.661} & \text{70.5} & \text{0.627}\\ \text{74.5} & \text{0.641} & \text{72.1} & \text{0.631}\\ \text{74.0} & \text{0.637} & \text{71.2} & \text{0.641}\\ \text{72.4} & \text{0.630} & \text{73.0} & \text{0.631}\\ \text{75.2} & \text{0.644} & \text{72.7} & \text{0.634}\\ \text{76.0} & \text{0.639} & \text{71.4} & \text{0.638}\\ \end{matrix}$$

Consider the Minitab output shown below.

$$\begin{matrix} \text{Test and CI for One Proportion}\\ \text{Test of p = 0.3 vs p not = 0.3}\\ \text{Sample} & \text{X} & \text{N} & \text{Sample p} & 95\% CI & \text{Z-Value} & \text{P-Value}\\ \text{1} & \text{95} & \text{250} & \text{0.380000} & \text{(0.319832, 0.440168)} & \text{2.76} & \text{0.006}\\ \end{matrix}$$

(a) Is this a one-sided or a two-sided test? (b) Was this test conducted using the normal approximation to the binomial? Was that appropriate? (c) Can the null hypothesis be rejected at the 0.05 level? (d) Can the null hypothesis $H_{0} : p=0.4 \text { versus } H_{0} : p \neq 0.4$ be rejected at the 0.05 level? How can you do this without performing any additional calculations? (e) Construct an approximate 90% traditional CI for p.

For each of the following designs, answer the following questions. (a) Compute the estimates of the effects and their standard errors for this design. (b) Construct two-factor interaction plots and comment on the interaction of the factors. (c) Use the t ratio to determine the significance of each effect with $\alpha = 0.05.$ Comment on your findings. (d) Compute an approximate 95% CI for each effect. Compare your results with those in part (c) and comment. (e) Perform an analysis of variance of the appropriate regression model for this design. Include in your analysis hypothesis tests for each coefficient, as well as residual analysis. State your final conclusions about the adequacy of the model. Compare your results to part (c) and comment. An article in the Journal of Testing and Evaluation (Vol. 16, No. 6, 1988) investigated the effects of cyclic loading frequency and environmental conditions on fatigue crack growth at a constant 22 MPa stress for a particular material. Some of the data from the experiment are shown here. The response variable is fatigue crack growth rate. Frequency

$$\begin{matrix} \quad & \quad & \text{Environment}\\ \quad & H_2O & \text{Salt} H_2O\\ \quad & \text{2.06} & \text{1.90}\\ \text{10} & \text{2.05} & \text{1.93}\\ \quad & \text{2.23} & \text{1.75}\\ \quad & \text{2.03} & \text{2.06}\\ \quad & \quad & \quad\\ \quad & \text{3.20} & \text{3.10}\\ \quad & \text{3.18} & \text{3.24}\\ \text{1} & \text{3.96} & \text{3.98}\\ \quad & \text{3.64} & \text{3.24}\\ \end{matrix}$$

The 6-kg circular disk and attached shaft rotate at a constant speed $\omega$ = 10 000 rev/min. If the center of mass of the disk is 0.05 mm off center, determine the magnitudes of the horizontal forces A and B supported by the bearings because of the rotational imbalance.

Concern the implicit function theorems and the inverse function theorem. Suppose that F(u, v) is of class $C^1$ and is such that $F(−2, 1) = 0$ and $F_u (−2, 1) = 7, F_v(−2, 1) = 5$. Let $G(x, y, z)=F\left(x^{3}-2 y^{2}+z^{5}, x y-x^{2} z+3\right)$. (a) Check that $G(−1, 1, 1) = 0$. (b) Show that we can solve the equation G(x, y, z) = 0 for z in terms of x and y (i.e., as z = g(x, y), for (x, y) near (−1, 1) so that g(−1, 1) = 1).

Consider the patient satisfaction survey data (a) Estimate the mean satisfaction given that age = 24, severity = 38, Surg-Med = 0, and anxiety = 2.8. (b) Compute a 95% CI on this mean response. (c) Compute a 95% PI on a future observation at the same values of the regressors. (d) What do you notice about the relative size of these two intervals? Which is wider and why? Use Minitab to assist you in answering the following. (a) Estimate the regression coefficients. Write the multiple linear regression model. Comment on the relationship found between the set of independent variables and the dependent variable. (b) Compute the residuals. (c) Compute $SS_E$ and estimate the variance. (d) Compute the coefficient of determination, $R^2,$ and adjusted coefficient of multiple determination, $R_{\text { Adjusted }}^{2}.$ Comment on their values. (e) Construct the ANOVA table and test for significance of regression. Comment on your results. (f) Find the standard error of the individual coefficients. (g) Use a t-test to test for significance of the individual coefficients at $\alpha=0.05.$ Comment on your results. (h) Construct 95% CIs on the individual coefficients. Compare your results with those found in part (g) and comment. (i) Perform a model adequacy check, including computing studentized residuals and Cook's distance measure for each of the observations. Comment on your results. (j) Compute the variance inflation factors and comment on the presence of multicollinearity. Data from a patient satisfaction survey in a hospital are shown in the following table:

$$\begin{matrix} \text{Observation} & \text{Age} & \text{Severity } & \text{Surg-Med} & \text{Anxiety} & \text{Satisfaction}\\ \text{1} & \text{55} & \text{50} & \text{0} & \text{2.1} & \text{68}\\ \text{2} & \text{46} & \text{24} & \text{1} & \text{2.8} & \text{77}\\ \text{3} & \text{30} & \text{46} & \text{1} & \text{3.3} & \text{96}\\ \text{4} & \text{35} & \text{48} & \text{1} & \text{4.5} & \text{80}\\ \text{5} & \text{59} & \text{58} & \text{0} & \text{2.0} & \text{43}\\ \text{6} & \text{61} & \text{60} & \text{0} & \text{5.1} & \text{44}\\ \text{7} & \text{74} & \text{65} & \text{1} & \text{5.5} & \text{26}\\ \text{8} & \text{38} & \text{42} & \text{1} & \text{3.2} & \text{88}\\ \text{9} & \text{27} & \text{42} & \text{0} & \text{3.1} & \text{75}\\ \text{10} & \text{51} & \text{50} & \text{1} & \text{2.4} & \text{57}\\ \text{11} & \text{53} & \text{38} & \text{1} & \text{2.2} & \text{56}\\ \text{12} & \text{41} & \text{30} & \text{0} & \text{2.1} & \text{88}\\ \text{13} & \text{37} & \text{31} & \text{0} & \text{1.9} & \text{88}\\ \text{14} & \text{24} & \text{34} & \text{0} & \text{3.1} & \text{102}\\ \text{15} & \text{42} & \text{30} & \text{0} & \text{3.0} & \text{88}\\ \text{16} & \text{50} & \text{48} & \text{1} & \text{4.2} & \text{70}\\ \text{17} & \text{58} & \text{61} & \text{1} & \text{4.6} & \text{52}\\ \text{18} & \text{60} & \text{71} & \text{1} & \text{5.3} & \text{43}\\ \text{19} & \text{62} & \text{62} & \text{0} & \text{7.2} & \text{46}\\ \text{20} & \text{68} & \text{38} & \text{0} & \text{7.8} & \text{56}\\ \text{21} & \text{70} & \text{41} & \text{1} & \text{7.0} & \text{59}\\ \text{22} & \text{79} & \text{66} & \text{1} & \text{6.2} & \text{26}\\ \text{23} & \text{63} & \text{31} & \text{1} & \text{4.1} & \text{52}\\ \text{24} & \text{39} & \text{42} & \text{0} & \text{3.5} & \text{83}\\ \text{25} & \text{49} & \text{40} & \text{1} & \text{2.1} & \text{75}\\ \end{matrix}$$

The regressor variables are the patient's age, an illness severity Index (larger values indicate greater severity), an indicator variable denoting whether the patient is a medical patient (0) or a surgical patient (1), and an anxiety index (larger values indicate greater anxiety)

Solve each equation. $e^{4 x} \cdot e^{x^{2}}=e^{12}$

An article in the Journal of the Environmental Engineering Division (“Least Squares Estimates of BOD Parameters,” Vol. 106, 1980, pp. 1197–1202) describes the results of testing a sample from the Holston River below Kingport, TN, during August 1977. The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting data is shown here:

$$\begin{matrix} \text{Time (days):} & \text{1} & \text{2} & \text{4} & \text{6} & \text{8} & \text{10} & \text{12} & \text{14} & \text{16}\\ \quad & \text{18} & \text{20}\\ \text{BOD (mg/liter):} & \text{0.6} & \text{0.7} & \text{1.5} & \text{1.9} & \text{2.1} & \text{2.6} & \text{2.9} & \text{3.7} & \text{3.5}\\ \quad & \text{3.7} & \text{3.8}\\ \end{matrix}$$

(a) Assuming that a simple linear regression model is appropriate, fit the regression model relating BOD ( y) to the time (x). What is the estimate of $\sigma^2?$ (b) What is the estimate of expected BOD level when the time is 15 days? (c) What change in mean BOD is expected when the time increases by 3 days? (d) Suppose the time used is 6 days. Calculate the fitted value of y and the corresponding residual. (e) Calculate the fitted $\hat{y}_{i}$ for each value $x_i$ of used to fit the model. Then construct a graph of $\hat{y}_{i}$ versus the corresponding observed values $y_i$ and comment on what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line. Does the plot actually obtained indicate that time is an effective regressor variable in predicting BOD?