(1)The file 'Soda.csv' contains survey responses from 339 adults regarding the % of daily liquid intake that is soda ('Soda'), whether or not they are on a diet ('Diet'), their gender ('Gender') and age in years ('Age'). Consider the sample to be random and representative of all US adults. After reading the data into the data frame soda the table() function give the following summary information of the variable 'Diet' versus 'Gender':

Perform a test for whether the population proportion of females on a diet is different from the population proportion of males on a diet. What conclusion do you reach? Why do you reach that conclusion? What does the associated confidence interval tell you? Are the assumptions behind the test and interval satisfied? (R command)

Soda.csv:

Soda Diet Gender Age 10 No Male 19 25 No Female 32 20 No Male 14 0 No Male 18 90 No Female 17 0 Yes Female 40 0 Male 20 0 Female 19 40 Yes Female 22 1 No Male 25 0 Female 36 10 Yes Male 20 50 No Female 21 0 Female 21 5 Yes Male 59 5 No Male 36 0 Male 37 50 No Male 40 2 Yes Female 24 60 No Male 20 50 Yes Male 40 10 Yes Male 28 0 Male 30 1 Male 34 4 Yes Male 15 10 Yes Male 21 70 Yes Female 19 No Male 23 0 No Male 42 0 Yes Male 44 0 Female 56 1 Yes Male 32 3 Yes Female 28 45 Yes Female 46 20 Yes Female 31 15 No Male 21 Male 65 90 Yes Female 28 0 Male 24 10 No Male 59 0 Female 20 6 No Male 16 0 Female 30 40 Yes Female 18 67 Yes Female 24 15 No Male 25 20 Yes Female 39 0 No Female 15 80 No Female 32 5 Yes Male 25 85 No Male 21 0 Yes Female 18 12 No Male 22 0 Female 41 5 No Female 49 20 No Male 19 0 No Female 34 75 No Male 33 2 No Female 14 50 No Female 24 90 No Male 32 12 No Female 61 1 Yes Male 62 0 Female 28 0 Yes Male 34 0 Male 57 10 Yes Male 38 1 No Female 32 20 No Male 31 40 Yes Female 27 90 Yes 19 0 Female 21 0 Male 15 0 Female 59 0 No Female 49 7 Yes Female 24 1 Yes Female 49 10 No Female 29 44 No Male 36 15 No Male 21 5 No Male 18 2 Female 55 0 Female 20 0 No Male 43 2 No Female 41 2 No Female 41 10 Yes Female 35 40 No Female 39 0 Male 28 0 Yes Female 8 No Female 19 20 No Female 20 15 No Male 22 0 Female 60 10 Yes Male 40 1 Yes Female 19 5 No Female 20 0 Female 19 70 No Female 20 0 Male 61 0 Female 46 0 Male 21 5 No Female 20 2 No Male 23 5 Yes Female 48 1 No Female 20 0 Male 19 50 Yes Female 44.95 0 Female 43 6 No Male 26 30 No Male 26 10 No Male 20 2 No Female 21 5 No Female 26 1 Yes Female 18 0 No Female 44 0 Female 26 90 Yes Female 31 20 No Male 16 0 Female 61 60 No Female 19 50 Yes Female 39 20 Yes Male 25 0 Female 20 50 Yes Female 20 0 Female 19 1 No Male 21 5 Yes Female 19 1 No Male 19 2 Yes Female 49 65 No Female 19 0.1 No Male 0 Male 44 50 No Female 15 95 Yes Female 37 20 No Male 31 8 Male 25 50 Yes Female 54 0 Male 58 10 Yes Female 43 0 Female 23 2 No Female 24 50 No Female 20 85 No Female 18 0 Female 40 0 Female 44 2 No Male 40 10 Yes Female 55 2 No Male 43 3 No Female 23 0 Male 19 5 No Male 39 0 No Male 23 25 No Female 18 5 No Male 78 90 No Male 21 55 Yes Male 42 58 No Male 19 60 Yes Female 29 25 Yes Male 46 0 35 5 No Female 19 0 No Female 24 30 No Female 25 1 No Female 21 15 Yes Male 20 15 No Male 25 2 No Female 19 0 No Female 62 0 Female 20 60 Yes Male 48 0 Female 31 70 Yes Male 22 80 No Female 24 20 No Male 20 10 No Male 18 0 No Female 21 0 No Female 29 0 Female 19 96 Yes Male 39 5 No Male 19 0 Male 18 85 No Male 41 40 Yes Female 18 80 No Female 20 0 Female 29 10 No Female 18 5 No Male 17 0 Female 37 0 Yes Female 27 50 Yes 56 60 Yes Female 27 0 Female 16 20 Yes Female 54 0 Male 24 0 Male 49 0 Male 19 0 Female 21 25 No Male 20 1 Yes Female 19 95 Yes Male 54 2 No Female 21 50 No Female 22 10 No Female 20 75 No Male 21 0 Yes Male 20 0 No Female 17 0 Male 22 25 Yes Male 67 0 No Male 42 0 Yes Female 50 0 Yes Female 50 0 No Male 20 50 Yes Female 55 3 No Female 30 0 Female 42 70 Yes Female 22 65 No Male 20 0 No Male 42 0 No Female 19 0 No Male 89 30 No Male 27 0 No Male 23 33 No Male 38 90 No Male 24 10 No Male 21 5 No Male 20 89 No Male 30 4 No Male 29 50 Female 27 0 Female 18 5 No Male 21 2 Yes Female 26 0 Female 40 1 No Male 32 3 No Male 48 15 Yes Female 54 35 No Male 16 10 Yes Male 46 0 Male 45 1 No Female 18 75 No Male 25 60 No Male 27 10 No Male 35 0 No Male 43 0 No Male 20 0 No Female 50 0 No Male 17 60 No Female 35 0 Male 40 60 No Male 19 0 Male 21 No Male 2 No Female 17 5 Yes Male 25 30 Yes Male 21 3 Yes Female 35 35 No Male 19 0 Yes Male 47 1 No Female 30 0 No Male 20 25 Yes Female 19 12 Yes Female 32 25 No Female 30 0 Male 48 0 No Male 20 20 No Male 18 0 Male 28 35 No Female 18 7 No Male 16 0 No Male 29 0 Yes Male 19 0 Female 22 5 No Male 21 50 Yes Female 23 25 No Female 12 15 No Female 28 24 No Male 31 10 Yes Female 51 5 Yes Male 49 30 Yes Female 43 0 Yes Female 29 10 No Female 32 3 Yes Female 50 90 Yes Female 54 0 Male 18 10 Male 49 Male 33 5 Yes Male 50 0 No Male 31 0 No Male 19 5 No Male 65 90 No Male 17 0 Female 18 20 No Male 18 97 No Male 19 0 Yes Female 25 0 No Female 19 10 No Male 34 0 Female 21 25 Yes Female 22 1 Yes Male 52 0 Male 57 10 No Female 18 0 Female 19 0 Male 29 10 Yes Female 25 95 Yes Female 40 75 Yes Male 56 10 Yes Male 20 45 No Female 19 4 Yes Female 73 50 Yes Female 44 0 No Female 21 1 No Male 19 0 Male 28 5 No Male 18 0 Male 17 45 No Female 18 10 No Male 46 100 Yes Male 46 75 No Female 18 10 No Female 19 0 Female 19 20 No Male 22 75 No Female 32 3 No Male 19 10 Yes Female 47 5 No Male 27 3 Yes Male 21 0 No Female 18 25 No Male 19 0 Male 23 10 No Female 53 0 Male 27 5 Yes Male 19 25 No Male 18 15 No Female 20 80 No Female 18