The dataset below that contains information on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions as well as cars with other transmissions. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? 1. Set up the null and alternative hypotheses. 2. Compute the test statistic. 3. State the p-value for the test. State the decision and conclusion of the test in context. Feel free to use excel, Rstudio, or any other methods to answer the Question! Thanks Auto Manual 77 22 126 30 52 28 62 26 62 29 106 20 27 27 28 22 24 26 26 26 30 26 21 23 21 28 23 29 25 25 20 25 20 22 18 17 17 27 14 25 15 19 18 27 17 30 14 23 18 24 17 23 14 22 15 23 18 24 17 27 14 23 19 22 17 25 17 19 14 26 16 21 16 23 14 18 17 18 17 18 14 18 16 19 16 19 14 21 18 18 15 18 14 18 14 23 15 20 14 23 14 23 13 23 14 23 13 24 15 19 13 22 13 22 13 21 13 11 13 13 12 11 13 12 12 11 12 12 15 23 13 19 13 16 13 14 13 15 13 31 13 12 13 12 12 21 11 22 13 29 13 27 21 27 22 27 13 25 19 25 16 18 19 18 22 19 15 19 19 19 21 19 20 19 22 19 28 11 29 11 12 18 12 17 18 29 16 27 14 27 18 27 16 25 15 25 14 18 18 17 16 18 15 18 14 18 23 18 20 18 12 17 12 17 28 18 18 18 17 18 15 18 17 18 15 16 17 16 14 21 15 14 16 18 13 18 13 18 15 20 12 19 12 17 10 18 10 17 18 19 16 19 18 19 23 18 18 18 17 13 13 14 12 29 15 19 16 17 17 15 19 21 16 17 18 16 22 17 17 19 16 27 12 27 17 25 16 23 12 18 12 14 14 21 15 21 17 21 19 18 10 23 10 20 10 15 10 15 10 17 27 16 27 14 19 29 18 17 19 22 17 30 13 28 13 24 15 22 19 30 18 20 19 27 30 27 25 26 23 25 30 26 26 20 20 20 19 20 20 23 19 17 23 20 29 21 35 23 26 23 23 21 27 30 22 19 24 21 35 22 18 30 18 21 18 17 20 20 22 15 24 20 12 19 27 16 26 14 29 26 27 25 15 28 13 15 15 14 14 22 14 22 16 29 17 17 15 25 15 22 13 24 15 27 15 21 12 18 14 24 13 21 15 20 16 19 14 18 15 31 12 24 12 21 10 17 10 17 10 14 10 27 10 26 10 25 11 25 11 20 11 20 10 17 11 22 11 22 11 30 10 16 17 16 17 15 17 15 19 21 18 19 17 21 17 20 14 21 14 18 15 20 15 17 15 16 10 20 20 16 17 15 22 19 22 15 17 19 17 19 17 19 14 19 17 21 21 19 14 20 17 17 15 14 15 14 10 22 22 17 17 20 20 23 22 17 14 21 22 20 22 22 14 16 13 13 13 16 20 20 16 16 15 15 15 10 16 13 16 20 18 13 16 16 15 13 15 13 10 20 20 16 16 20 20 21 16 13 21 21 18 21 21 13 14 12 23 20 19 19 20 20 20 20 20 20 18 18 19 18 18 18 18 18 18 19 19 19 19 19 16 17 16 17 21 19 13 13 19 19 19 20 19 19 16 17 21 17 18 20 20 19 13 15 15 17 16 16 20 19 21 16 16 21 15 15 15 19 18 18 16 16 15 15 19 15 16 12 17 13 12 16 17 20 15 14 16 18 24 24 23 22 19 18 19 18 15 19 17 17 16 22 16 20 15 34 34 14 13 13 13 13 13 13 29 29 16 28 28 28 28 29 18 17 14 14 14 14 27 36 22 22 44 41 43 35 30 28 27 23 22 23 23 25 23 53 25 41 41 27 23 43 40 51 23 22 27 27 23 23 44 20 20 20 20 19 20 20 34 20 23 21 23 21 18 23 20 20 30 20 20 21 20 21 20 18 17 22 22 28 35 110 23 20 26 23 22 23 20 19 24 24 22 27 25 32 23 25 30 22 23 35 41 19 20 20 21 22 21 19 16 17 18 22 19 19 24 22 21 22 18 22 27 21 16 21 19 20 17 18 17 13 18 16 17 17 17 23 12 15 11 21 28 27 26 26 13 12 13 16 15 15 16 20 19 28 27 26 26 13 16 23 11 12 18 18 18 18 17 18 18 18 25 20 21 18 19 27 26 22 22 22 12 21 18 12 15 27 25 28 25 25 23 11 11 18 18 19 23 22 17 30 24 24 24 30 23 24 18 20 17 20 18 11 25 17 17 16 18 19 25 19 19 18 12 18 18 26 22 22 22 17 27 17 18 22 18 20 15 16 19 17 18 28 18 18 17 25 21 30 22 20 18 20 17 17 15 14 14 14 14 14 14 14 17 17 18 16 15 15 15 17 16 17 11 11 19 22 30 21 18 17 18 12 18 18 18 18 29 24 16 13 17 15 15 14 15 12 16 14 11 14 13 13 19 18 17 19 19 18 18 17 19 18 17 19 18 20 14 13 21 19 22 19 19 16 16 16 18 19 12 12 16 18 17 17 16 15 12 12 12 18 12 13 15 18 16 17 17 16 19 15 17 13 13 13 20 18 21 17 18 17 18 16 17 17 8 11 19 18 20 20 20 19 17 18 18 17 17 14 14 17 19 18 18 20 19 19 18 27 18 17 16 16 17 17 16 14 16 14 14 21 21 16 21 23 21 23 15 15 15 19 18 18 11 21 21 15 15 17 16 16 16 16 18 14 19 18 15 15 13 17 13 13 21 20 20 17 16 19 19 16 14 16 14 16 19 16 20
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The dataset below that contains information on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions as well as cars with other transmissions. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city
mileage?
1. Set up the null and alternative hypotheses.
2. Compute the test statistic.
3. State the p-value for the test. State the decision and conclusion of the test in context.
Feel free to use excel, Rstudio, or any other methods to answer the Question! Thanks
Auto | Manual |
77 | 22 |
126 | 30 |
52 | 28 |
62 | 26 |
62 | 29 |
106 | 20 |
27 | 27 |
28 | 22 |
24 | 26 |
26 | 26 |
30 | 26 |
21 | 23 |
21 | 28 |
23 | 29 |
25 | 25 |
20 | 25 |
20 | 22 |
18 | 17 |
17 | 27 |
14 | 25 |
15 | 19 |
18 | 27 |
17 | 30 |
14 | 23 |
18 | 24 |
17 | 23 |
14 | 22 |
15 | 23 |
18 | 24 |
17 | 27 |
14 | 23 |
19 | 22 |
17 | 25 |
17 | 19 |
14 | 26 |
16 | 21 |
16 | 23 |
14 | 18 |
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14 | 21 |
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15 | 18 |
14 | 18 |
14 | 23 |
15 | 20 |
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14 | 23 |
13 | 24 |
15 | 19 |
13 | 22 |
13 | 22 |
13 | 21 |
13 | 11 |
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13 | 12 |
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12 | 12 |
15 | 23 |
13 | 19 |
13 | 16 |
13 | 14 |
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13 | 31 |
13 | 12 |
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11 | 22 |
13 | 29 |
13 | 27 |
21 | 27 |
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13 | 25 |
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15 | 19 |
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28 | 11 |
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11 | 30 |
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