Calculating a $95 \%$ confidence interval $(95 \% \mathrm{Cl})$ provides a good estimate of how close the sample mean is to the true mean. The mean $\pm$ the $95 \%$ $\mathrm{Cl}$ gives the $95 \%$ confidence limits. On average, 95 times out of 100 , the true population mean will lie within the confidence limits. The $95 \% \mathrm{Cl}$ can be plotted onto graphs to determine significance. If they overlap there is no significant difference between the data. The $95 \% \mathrm{Cl}$ for student $\mathrm{A}$ is $1.27$ and for student $\mathrm{B}$ is $2.37$ at $\mathrm{p}=0.05$.

(a) Plot the mean dispensing volume and $95 \% \mathrm{Cl}$ for both sets of data on the grid right). Plot as a column graph with error bars.

(b) Is the difference significant? Why or why not?

Indicate how the graph of each function is related to the graph of one of the six basic functions. Sketch a graph of each function.

f(x) = (x+3) squared + 3

Previously, an organization reported that teenagers spent $4.5$ hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was $4.75$ hours with a sample standard deviation of $2.0$. Conduct a hypothesis test, the Type I error is:

a. to conclude that the current mean hours per week is higher than $4.5$, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than $4.5$, when in fact, it is the same

c. to conclude that the mean hours per week currently is $4.5$, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than $4.5$, when in fact, it is not higher

Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.

3 times the sum of $x$ and $y$ squared plus 5 times the difference of $2 x$ and $y$

Find the area of the surface S.

S is the part of the surface z=1/2 x squared +y that lies above the triangular region with vertices (0,0), (1,3), and (0,3).

Write each of the following statements as a mathematical expression. State whether the expression is nonlinear. If it is nonlinear, then explain why.

1. A number decreased by three squared

Solve the initial-value problems.

a. dy/dx= cos x - 5e raised to x,\ y(0)=0.

b.dy/dx= xe raised to (x squared),\ y(0)=0.

Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.

The product of 9 and $t$ squared, increased by the sum of the square of $t$ and 2

For the following question,

Use the given transformation to graph the function. Note the vertical and horizontal asymptotes.

The reciprocal squared function shifted to the right $2$ units.

Which is NOT a way to express 8$^2$?

A. eight multiplied by two

B. eight to the second power

C. eight squared

D. eight times eight

What is the difference between a Type I error and a Type I error?

Referring to an exercise before, regard the sample of five trial runs (which has standard deviation $19.65$) as a preliminary sample. Determine the number of trial runs of the chemical process needed to make us:

$95$ percent confident that $\bar{x}$, the sample mean hourly yield, is within a margin of error of eight pounds of the population mean hourly yield $\mu$ when catalyst $\text{XA}-100$ is used.

Find exact solutions (x real and theta in degrees).

2 cos squared theta + 3 sin theta = 0, theta in [0 deg, 360 deg)

Describe the alkaline error in the measurement of $\mathrm{pH}$. Under what circumstances is this error appreciable? How are $\mathrm{pH}$ data affected by alkaline error?