Problem

In a completely randomized experimental design, t…

Problem 44 Hard Difficulty

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$?$

Answer

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

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Intro Stats / AP Statistics

Essentials of Modern Business Statistics

Chapter 10

Comparisons Involving Means, Experimental Design, and Analysis of Variance

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Video Transcript

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

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