Question

You may need to use the appropriate technology to answer this question. The Wall Street Journal's Shareholder Scoreboard tracks the performance of 1,000 major U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the re investment of dividends. Ratings are assigned by dividing all 1,000 companies into five groups from A (top 20%), B (next 20%), to E (bottom 20%). Shown here are the one-year ratings for a sample of 60 of the largest companies. A B C D E 5 7 15 20 13 Do the largest companies differ in performance from the performance of the 1,000 companies in the Shareholder Scoreboard? Use ? = 0.05. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value =

          You may need to use the appropriate technology to
answer this question.
The Wall Street Journal's Shareholder Scoreboard
tracks the performance of 1,000 major U.S. companies. The
performance of each company is rated based on the annual total
return, including stock price changes and the re investment of
dividends. Ratings are assigned by dividing all 1,000 companies
into five groups from A (top 20%), B (next 20%), to E (bottom 20%).
Shown here are the one-year ratings for a sample of 60 of the
largest companies.
A
B
C
D
E
5
7
15
20
13
Do the largest companies differ in performance from the
performance of the 1,000 companies in the Shareholder Scoreboard?
Use 
? = 0.05.
Find the value of the test statistic. (Round your answer to
three decimal places.)
Find the p-value. (Round your answer to four
decimal places.)
p-value =

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Added by Ignacio A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

04/18/2022

Step 1

Given: Observed values: 5, 7, 15, 20, 13 Expected value for each rating: 12 Calculating for each rating: \[ \chi^2 = \frac{(5 - 12)^2}{12} = 4.0833 \] \[ \chi^2 = \frac{(7 - 12)^2}{12} = 2.0833 \] \[ \chi^2 = \frac{(15 - 12)^2}{12} = 0.75 \] \[ \chi^2 = Show more…

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You may need to use the appropriate technology to answer this question. The Wall Street Journal's Shareholder Scoreboard tracks the performance of 1,000 major U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the re investment of dividends. Ratings are assigned by dividing all 1,000 companies into five groups from A (top 20%), B (next 20%), to E (bottom 20%). Shown here are the one-year ratings for a sample of 60 of the largest companies. A B C D E 5 7 15 20 13 Do the largest companies differ in performance from the performance of the 1,000 companies in the Shareholder Scoreboard? Use ? = 0.05. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value =

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00:01 It is given that for 1 ,000 companies based on their ratings, they are grouped as a, b, c, d and e.

00:13 A as the top 20 percentage of companies and b as the next 20 percentage of companies.

00:22 Similarly, e as the last 20 percentage of companies and a sample of 60 % of companies.

00:30 Largest companies are taken and the number of companies based on ratings are 5 ,7, 15, 20 and 13.

00:45 The alpha level is given as 5 percentage or 0 .05.

00:52 Now we have to find that if the sampled largest companies differ, by their performance.

01:05 The nell hypothesis is such that pfa equal to pfb equal to pfc equal to pfc equal to pfd equal to pfe of e and the alternative hypothesis is such that at least one of the largest companies which are sampled differ by their performance and kai square goodness of it is used to test this null hypothesis.

01:35 Let us represent observed values as oi and the expected values as ei.

01:41 It is given that each ratings has 20 percentage of companies.

01:46 This implies that for a sample of 60, the 20 percentage which is 60 into 0 .2, that is 12.

01:55 Now the expected value for each of the ratings are 12 companies.

02:01 The test statistics for the kai square goodness of it is summation oi minus ei, the old square divided by ei.

02:14 It is known as for the ratings of a, b, c, d and e.

02:23 The observed values are 5, 7, 15, 20 and 13...

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