Related questions with answers

The following table provides information on the 10 NASDAQ companies with the largest percentage of their stocks traded on July 6, 2009. Specifically, the table gives the information on the percentage of stocks traded and the change (in dollars per share) in each stock's price.

Stock	Percentage Traded	Change ($)
Matrixx	19.6	-0.43
SpectPh	14.7	-1.10
DataDom	12.4	0.85
CardioNet	9.3	-0.11
DryShips	9.0	-0.42
DynMatl	8.0	-1.16
EvrgrSlr	7.9	-0.04
EagleBulk	7.9	-0.11
Palm	7.8	-0.02
CentAl	7.4	-0.57

a. With percentage traded as an independent variable and the change in the stock's price as a dependent variable, compute $S S_{x x}, S S_{y y}$ , and $S S_{x y}$ .

b. Construct a scatter diagram for these data. Does the scatter diagram exhibit a negative linear relationship between the percentage of stock traded and the change in the stock's price?

c. Find the regression equation$ $\hat{y}$ =a+b x$.

d. Give a brief interpretation of the values $a$ and $b$ calculated in part$ $\mathrm{c}.

e. Compute the correlation coefficient $r$ .

f. Predict the change in a stock's price if $8.6 \%$ of the stock's shares are traded on a day. Using part b, how reliable do you think this prediction will be? Explain.

Approximate the slope of the tangent line (instantaneous rate of change) for the function $f(x)=5^{x}-x^{3}$ at x = 1.

Above the indefinite pronoun in each sentence, write S if it is singular or P if it is plural. Then, underline the correct form of the verb in parentheses.

Example: $\overset{\textit{\color{#c34632}{S}}}{{\text{Everyone}}}$ who likes vegetables (enjoy, $\underline{{enjoys}}$ ) this meal.

Everyone, including the movie critics, (raves, rave) about her latest movie.

Question

A coin is tossed 500 times. True or false, and explain. a) The SE for the percentage of heads among the 500 tosses is 2.2 percentage points. b) The SE for the percentage of tails among the 500 tosses is 2.2 percentage points. c) The SE for the difference
$\begin{array} { c } { \text { percentage of heads - percentage of tails } } \\ { \text { is } \sqrt { 2.2 ^ { 2 } + 2.2 ^ { 2 } } \approx 3.1 \text { percentage points. } } \end{array}$

Solution

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Step 1

1 of 6

Given:

\begin{align*} \text{Sample size}&=500 \end{align*}

(a) Let 0 represent tails and let 1 represent heads.

Since we expect heads and tails to be equally likely to occur by chance, we use a box containing a single 0 and a single 1.

Next, we determine the standard deviation of the values in the box. The standard deviation is the square root of the squared deviations from the mean divided by the sample size decreased by 1: