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Nasee Market Analytics provides services to investors withforecasts of the movement of the stock market. For a recentforecast, the mean percentage change in the sto...

Question

Nasee Market Analytics provides services to investors withforecasts of the movement of the stock market. For a recentforecast, the mean percentage change in the stock price of 52recommended stocks was -19.9 and the standard deviation was 18.6.What is the percentage change below which only 5% of the stocksrecommended fell?

Nasee Market Analytics provides services to investors with forecasts of the movement of the stock market. For a recent forecast, the mean percentage change in the stock price of 52 recommended stocks was -19.9 and the standard deviation was 18.6. What is the percentage change below which only 5% of the stocks recommended fell?



Answers

A sample survey of 54 discount brokers showed that the mean price charged for a trade of
100 shares at $\$ 50$ per share was $\$ 33.77$ (AAII Journal, February $2006 ) .$ The survey is con-
ducted annually. With the historical data available, assume a known population standard
deviation of $\$ 15 .$
$$
\begin{array}{l}{\text { a. Using the sample data, what is the margin of emor associated with a } 95 \% \text { confidence }} \\ {\text { interval? }} \\ {\text { b. Developa } 95 \% \text { confidence interval for the mean price charged by discount brokers for }} \\ {\text { a trade of } 100 \text { shares at } \$ 50 \text { per share. }}\end{array}
$$

We need to see the change from April 29th April 30th of GODHEAD included some very rich rough graphs of those sketches so that we can see what we actually care about. And what we care about is the close from here. Excuse me. To hear in this close is that $665 Where's this closes at $655 so we can see that the change as a monetary amount is negative. 10 Went back down by 10. And to find it as a percent, you need to take that 10 divided by this original value of 665. And that gives us a decimal of zero point 015 zero. And this has a percent. You just move that decimal two places over or multiplied by 100. However you want to think of it, but that would be 1.5%. And I'm gonna go ahead and make this all negative because it's going down 10. So it's negative 1.5% or negative. 10

We need to see the approximate change. And so what I think we need to care about is the closing of each to see how far this difference was. And so this closed on April 30th make sure that I got that date, right? Yep, April 30th at $655. And the other one? It's just a hair below 6 85 So I'm gonna call that 6 84 which means there was a positive change, just under 30 of $29 not a find that as a percent. We need to take $29 divided by original value of $655. And that's going to give us pretty ugly decimal that I encourage you guys to check with me. Let's see, let's seize 29. About about 6 55 is zero 0.0 for 42 And if we're going to change a suit, destiny, we need to move. Or to a percent. We need to move the decimal two places over or most by by 100. However, you prefer to think about it, meaning right that for a little bit nicer that there's a percent change of positive 4.4%

All right. This question gives us some information about companies and their profit goals. So part A wants us to provide a point estimate for the proportion of companies that fell short. Soapy hat equals the number of successes over end, which in this case, success means falling short. So it's 29 Tuvalu by 1 62 which comes out to be 0.1790 Then it wants us to compute the 95% confidence interval for the proportion that beat estimates. So P hat for the proportion that be elements is are estimates Rather same thing. The number that be 104 over the total 1 62 which is equal to 0.64 20 and then it once our margin of error, which is R Z value times the square root of P Hat Times Q hat all over end, which in this case are ze scores 1.96 because we have 95% confidence times or P Hat Times R Q. Hat all over our sample size, and our margin of error turns out to be proximately 0.73 a. Then our interval equals, he had closer minus error, which is pee hat, in this case, 0.642 plus or minus 0.738 And from there we get our interval with a lower bound of 0.5682 and an upper bound of 0.7158 Then it wants, if the margin of error his 0.5 it wants the sample size acquired. So remember that n equals he had times Q. Hat times R Z score over our margin of error squared, and we know all of these quantities. RP Hat is 0.642 r Q hat is 0.35 A r Z score is 1.96 and our air margin this 0.5 And if we work all this out, we'll get a decimal, which is 3 53.1 which we always round up in sample size calculations for margin of air, which in this case 3 50

In question 55 were given that the proportion of the investor population that has bullish sentiment about the stock market is 39% and were asked to use a recent sample of 450 investors, 41% of whom were bullish, to test the claim that the current proportion of investors that are bullish is significantly greater than the long term proportion of 39%. So right from the question we have some of her information we have the long term proportion is 0.39 and we also have a sample of 450 and the sample proportion is 0.41 So for part, they were asked to state our hypothesis to test the claim that the proportion in the current sample is greater than 39%. So the alternative hypothesis is that proportion is greater than 0.39 and the null hypothesis is that the proportion is less than or equal to you 0.39 and so in part B were as to use the sample to calculate the test statistic and the P value. So our test statistic is, uh, the first thing to note is that end times P is greater than or equal to five and end times. One minus p is also greater than or equal to five. And this tells us that once we satisfy this criteria, our test statistic follows the A normal distribution. Our sample proportions are normally distributed, so our test statistic is therefore it said no in her tested tested comes out the 0.87 Yeah, we should also note that this is an upper tail test because we're testing the claim that proportions air greater than 0.39 So if you go to the standard normal table, the couple value of 0.87 is this value right here? 0.8078 So this is the area to the left of our test statistic, and we want we're interested. R p values the area in the upper tail beyond the test statistics. So it's one minus this value, so we can say that he value is equal to one minus 0.8078 So that answers Part B and then part C is we're told at the significance level of Alfa equals 0.10 What is their conclusions regarding our test? So we can say that the T value is greater than Alva should finish calculating this year. A point 19 to you too is greater than Alfa. Therefore, we failed to reject the know head offices and we can state that we have insufficient evidence to justify the claim that the current population investors, um has a greater proportion than 39% were bullish about the market.


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