identify the claim and state $H_0$ and $H_a$.

Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. The well-being index is a way to measure how people are faring physically, emotionally, socially, and professionally, as well as to rate the overall quality of their lives and their outlooks, for the future. The table shows the well-being index scores for a sample of states from four regions of the United States. At $\alpha=0.10$, can you reject the claim that the mean score is the same for all regions?

$$\begin{matrix} \text{Northeast} & \text{Midwest} & \text{South} & \text{West}\\ \text{61.7} & \text{61.6} & \text{61.0} & \text{64.0}\\ \text{63.6} & \text{61.8} & \text{60.8} & \text{63.0}\\ \text{62.6} & \text{61.4} & \text{63.1} & \text{63.5}\\ \text{61.8} & \text{63.2} & \text{62.3} & \text{63.2}\\ \text{62.1} & \text{61.7} & \text{60.5} & \text{61.8}\\ \text{63.5} & \text{62.9} & \text{62.0} & \text{62.6}\\ \text{ } & \text{62.9} & \text{61.3} & \text{62.5}\\ \text{ } & \text{63.7} & \text{60.5} & \text{62.8}\\ \text{ } & \text{ } & \text{62.3} & \text{62.5}\\ \text{ } & \text{ } & \text{61.5} & \text{ }\\ \text{ } & \text{ } & \text{63.1} & \text{ }\\ \end{matrix}$$

The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is listed below. At $\alpha=0.01$, can you reject the dean's claim?

$$11.8 \quad 8.6 \quad12.6 \quad7.9\quad 6.4 \quad10.4 \quad13.6\quad 9.1$$

use technology to find the P-value

Let f be a constant function-that is, let f(x)=c, where c is some real number. Show that every number a gives rise to an absolute maximum and, at the same time, an absolute minimum of f.

(a) identify the claim and state $H_0$ and $H_a$. (b) decide whether to use a Wilcoxon signed-rank test or a Wilcoxon rank sum test. (c) find the critical value(s). (d) find the test statistic. (e) decide whether to reject or fail to reject the null hypothesis. (f) interpret the decision in the context of the original claim. A physician wants to determine whether an experimental medication affects an individual’s heart rate. The physician randomly selects 15 patients and measures the heart rate of each. The subjects then take the medication and have their heart rates measured after one hour. The table shows the results. At $\alpha=0.05$, can the physician conclude that the experimental medication affects an individual’s heart rate?

$$\begin{matrix} \text{Patient} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8}\\ \text{Heart rate (before)} & \text{72} & \text{81} & \text{75} & \text{76} & \text{79} & \text{74} & \text{65} & \text{67}\\ \text{Heart rate (after)} & \text{73} & \text{80} & \text{75} & \text{79} & \text{74} & \text{76} & \text{73} & \text{67}\\ \text{Patient} & \text{9} & \text{10} & \text{11} & \text{12} & \text{13} & \text{14} & \text{15} & \text{ }\\ \text{Heart rate (before)} & \text{76} & \text{83} & \text{66} & \text{75} & \text{76} & \text{78} & \text{68} & \text{ }\\ \text{Heart rate (after)} & \text{74} & \text{77} & \text{70} & \text{77} & \text{76} & \text{75} & \text{74} & \text{ }\\ \end{matrix}$$

Use logarithmic differentiation to find the derivative of the function. $y=x^{\ln x}$

Determine the intervals where the function $f(x)=\frac{\ln x}{x}$ is increasing and where it is decreasing.

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers r months after placing the line on the market was given by $D(t)=2000-1500 e^{-0.05 t}$ (t>0) Graph this function and answer the following question: What is the demand after 1 month? After 1 year? After 2 years? After 5 years?

For what value of c is the vector $\mathbf{v}=\langle 2,-5, c\rangle$ orthogonal to $\mathbf{w}=\langle 3,2,9\rangle$?

Your medical research team is investigating the mean cost of a 30-day supply of a certain heart medication. A pharmaceutical company thinks that the mean cost is less than $60. You want to support this claim. How would you write the null and alternative hypotheses?

Use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.

$$\begin{array}{l}2 x_{1}+5 x_{2}+12 x_{3}=6 \\ 3 x_{1}+x_{2}+5 x_{3}=12 \\ 5 x_{1}+8 x_{2}+21 x_{3}=17\end{array}$$

In each of parts (a) to (e) give the number of nonisomorphic abelian groups of the specified order-do not list the groups: (a) order 100, (b) order 576, (c) order 1155,(d) order 42875, (e) order 2704.

Lysozyme is an enzyme that cleaves cell walls. A 0.100-L sample of a solution of lysozyme that contains 0.0750 g of the enzyme exhibits an osmotic pressure of 1.32 $\times 10^{-3}$ atm at 25 $^{\circ} \mathrm{C}$. What is the molar mass of lysozyme?

Test the hypothesis using the classical approach. Be sure to verify the requirements of the test. $H_{0}: p=0.55$ versus $H_{1}: p<0.55$. $n=150 ; x=78 ; \alpha=0.1$

An electrical load has a power factor of 0.8 lagging. It dissipates 8 kW at a voltage of 200 V. Calculate the impedance of this load in rectangular coordinates.