💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Watch step-by-step video solution

Like

Report

In early $2009,$ the economy was experiencing a recession. But how was the recession affecting the stock market? Shown are data from a sample of 15 companies. Shown for each company is the price per share of stock on January 1 and April 30 (The Wall Street Journal, May $1,2009$ ).a. What is the change in the mean price per share of stock over the four-month period?b. Provide a 90$\%$ confident interval estimate of the change in the mean price per share of stock. Interpret the results.c. What was the percentage change in the mean price per share of stock over the four- month period?d. If this same percentage change were to occur for the next four months and again for the four months after that, what would be the mean price per share of stock at the end of the year 2009$?$

a. Decreases by $\$ 2.45$b. $-0.1720$ to 5.0720c. 7.97$\%$d. $\$ 23.95200389$

Intro Stats / AP Statistics

Chapter 10

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Descriptive Statistics

The Chi-Square Distribution

Experiment

Temple University

Missouri State University

Idaho State University

Lectures

0:00

07:23

The Dow Jones Industrial A…

01:31

06:21

A panel of economists prov…

03:21

Many investors and fimanci…

03:47

The stock market Some peop…

04:32

For the following exercise…

02:18

The following graph illust…

05:04

02:57

In January 2009 the unempl…

01:09

THE STOCK MARKET Refer to …

01:32

Volatility at the Pump The…

02:04

Dividend yield is the annu…

03:22

Consider the table in the …

05:08

The percentage of American…

06:56

Unemployment The number of…

06:54

Economists use labor-marke…

03:56

During 2008 the US economy…

04:38

The economy is in a recess…

04:43

An industry currently has …

01:18

THE STOCK MARKET For the w…

So this problem, the first thing we're asked to find is the change in the mean price per share of stock over the four month period. So that's simply the difference between the mean engine or the value in January. So, uh, I'll just call our first value X, um one in January, minus the value of that same X one in April. So it would be the value for applied materials in January. Honestly, Applied materials in April and you would take all these differences and then you would take some of these differences divided by our end. So you would take the some of the differences between X one are X in January X in April over, um, our sample size. So this is equal to we get a difference of negative 2.45 mean difference of negative 2.45 So that is our D bar negative 2.45 Next, we're as to find a interval of interval estimate of the difference between the two population means so basically a 90% 90% confidence interval. And that is what this formula here tells us. So our d bar, we just figured out to be native to 0.45 plus or minus. The tea, uh, are Alfa over to our Alfa is equal to one minus our confidence level, which is 10.9 or a conference interval, which is 0.9. So we have an Alfa of 0.10 point one. So a tea at Alfa over to appoint one is a t of 10.5 Given that we have a degrees of freedom of n minus one ridges equal 14 which is equal to for me Put up, we have a T value of 1.761 1.761 So 1.761 times a standard deviation of our differences which is equal two 4.73 over the squared of 15. So we get a confidence interval between negative 0.172 and 5.72 So we're 90% confident that the true difference of mean lies in between these two values and next we're asked to find a percent change. So the percent change is simply the, um the change in ah, the mean in January, Modest for the mean in January, minus the mean in April over the mean in April. Sorry, sorry, sorry. It is. I mean, in April, minus the mean in January Over the mean in January, you're finding percent change. So it's expected minus initial over the initial. This is our quote unquote expected. So are mean in April is equal to 28.28 Minus are mean in January, which is 30 point 73 over our mean in January of 30.73 Because we're looking for a percent will multiply all this by 100 so we get a value of negative 7.97 percent. So this is our percent change. And lastly, we are asked to find a projection of what should happen in the next four months and the next four months after that. So that would just be the value of the current stock in or the mean current stock in January. So that is 30 point 73 times. Um, and that value is going to be multiplied by, um one minus 10.0 seven nine. Right, because that is, um, this value Here, this translates 0.797 0.797 and this will be the value in April. So this should lead us to a mean in April. So this is our first period. In our second period, we're going to do the same thing. We're gonna take our mean in April and multiply it. But one minus 10.797 That should give us our mean for the next four months. So April, May, June, July. I think it's for July. Okay, so our mean for July. So basically, what we're doing is we're doing were multiplying this by this cubed. So it will be so. The projection is 30 0.73 times one minus 10.797 cubed just equal to approximately 23.95

View More Answers From This Book

Find Another Textbook

Numerade Educator

The Dow Jones Industrial Average (DJIA) underwent one of its infrequent resh…

The Dow Jones Industrial Average (DJIA) and the Standard \& Poor's …

A panel of economists provided forecasts of the U.S. economy for the first s…

Many investors and fimancial analysts believe the Dow Jones Industrial Avera…

The stock market Some people think that the behavior of the stock market in …

For the following exercise, consider the stock market crash in 1929 in the U…

The following graph illustrates how the price of a stock fluctuated from the…

In January 2009 the unemployment rate in all of New York City was $73 .$ The…

THE STOCK MARKET Refer to the graph below, which shows the earnings (and los…

Volatility at the Pump The graph shows the average price per gallon of gasol…

Dividend yield is the annual dividend per share a company pays divided by th…

Consider the table in the next column, which shows the change in inventories…

The percentage of American households that own publicly traded stocks began …

Unemployment The number of unemployed workers in the United States in recent…

Economists use labor-market data to evaluate how well an economy is using it…

During 2008 the US economy stopped growing and began to shrink. Table $1.25^…

The economy is in a recession with high unemployment and low output.a. D…

An industry currently has 100 firms, each of which has fixed cost of \$16 an…

THE STOCK MARKET For the week of January $5-9,2009,$ the Dow Jones Industria…

10:07

Visa Card USA studied bow frequently consumers of various age groups use pla…

03:17

In exercise 9 , an estimated regression equation was developed relating the …

02:15

FedEx and United Parcel Service (UPS) are the world's two leading cargo…

10:59

The U.S. Census Bureau computes quarterly vacancy and home ownership rates b…

02:20

The American Community Survey showed that residents of New York City have th…

09:00

If $X$ is a hypergeometric rv, show directly from the definition that $E(X)=…

07:32

A circular sampling region with radius $X$ is chosen by a biologist, where $…

02:28

In a survey, the planning value for the population proportion is $p^{*}=.35 …

04:58

Refer back to Example 4.54 . Because $n=4,$ the sample median is the average…

03:50

Is your favorite TV program often interupted by advertising? CNBC presented …