George Washington University Statistics Questions

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George Washington University

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problem 14 M&M answer link

https://www.slader.com/discussion/question/as-note...

problem 38 car origins

https://www.slader.com/textbook/9780321986498-stat...


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M & M’s As noted in an earlier chapter, Mars Inc. says that until very recently yellow candies made up 20% of its milk chocolate M&M's, red another 20%, and orange, blue, and green 10% each. The rest are brown. On his way home from work the day he was writing these exercises, one of the authors bought a bag of plain M&M's. He got 29 yellow ones, 23 red, 12 orange, 14 blue, 8 green, and 20 brown. Is this sample consistent with the company's stated proportions? Test an appropriate hypothesis and state your conclusion. a) If the M&M's are packaged in the stated proportions, how many of each color should the author have expected to get in his bag? b) To see if his bag was unusual, should he test goodness of-fit, homogeneity, or independence? c) State the hypotheses. d) Check the conditions. e) How many degrees of freedom are there? f) Find X2 and the P-value. g) State a conclusion. Car origins A random survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Are there differences in the national origins of cars driven by students and staff? Driver Student Staff American 107 105 European 33 12 Origin Asian 55 47 a) Is this a test of independence or homogeneity? b) Write appropriate hypotheses. c) Check the necessary assumptions and conditions. d) Find the P-value of your test. e) State your conclusion and analysis. Step-by-step solution 1. Step 1 of 8 (a) The distribution of counts of 2 groups on the same variable are being compared, the chisquare test of homogeneity can be used. Comment 2. Step 2 of 8 (b) The null hypothesis and alternative hypothesis are denoted by respectively. and There is no difference in the national origins of cars driven by staffs and students. There is a difference in the national origins of cars driven by staffs and students. Comment 3. Step 3 of 8 (c) The people were allotted to each of the groups in a random manner. Also, the treatment to each group was decided at random. All expected frequencies are greater than 5. Each of the data is counted. Comment 4. Step 4 of 8 (d) The table of observed counts are, Student Staff Total American 107 105 212 European 33 12 45 Asian 55 47 102 Total 195 164 359 Comment 5. Step 5 of 8 It can be observed that there are 3 rows and 2 columns. The number of degrees of freedom is given by: Where, The number of rows in the given table is denoted by r. And the number of columns in the given table is denoted by c. Therefore, the number of degrees of freedom is, Comment 6. Step 6 of 8 Next, the table of expected counts needs to be determined. The expected count for each cell is obtained as: Therefore, for the Student/American cell, the expected count is obtained as: Comment 7. Step 7 of 8 Proceeding in the above manner for each of the remaining five cells, we get the table of expected counts to be: Student Staff Total American 115.15 96.85 212 European 24.44 20.56 45 Asian 55.40 46.60 102 Total 195 164 359 Comment 8. Step 8 of 8 The chi-square value is obtained using the formula: Substituting the values from the tables of observed and expected counts, we get: Next, the P-value corresponding to and 2 degrees of freedom needs to be determined. This can be determined by using a tool like MS Excel (the CHIDIST ( ) function with the have: value and degrees of freedom as the parameters). Therefore, we (e) The P-value as determined above is low and hence the null hypothesis can be rejected. This implies that there is a difference in the national origins of cars driven by staffs and students. Comment
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Explanation & Answer

Here it is :)

M & M’s As noted in an earlier chapter, Mars Inc. says that until very recently
yellow candies made up 20% of its milk chocolate M&M's, red another 20%,
and orange, blue, and green 10% each. The rest are brown. On his way home
from work the day he was writing these exercises, one of the authors bought a
bag of plain M&M's. He got 29 yellow ones, 23 red, 12 orange, 14 blue, 8 green,
and 20 brown. Is this sample consistent with the company's stated proportions?
Test an appropriate hypothesis and state your conclusion.
a)

If the M&M's are packaged in the stated proportions, how many of
each color should the author have expected to get in his bag?
Yellow: 21
Red: 21
Orange: 11
Blue: 11
Green: 11
Brown...


Anonymous
Excellent resource! Really helped me get the gist of things.

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