Question

Using the data set (link below), please calculate a one-way chi-square tests for President Obama approval rating for the first years in office. Specifically run chi-square on the "Approving" column.

This is the information provided.

Approving
49
51
51
53
52
51
51
50
51
49
50
50
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51
49
48
48
48
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50
50
47
49
52
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49
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51
51
49
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49
49
49
48
49
49
50
50
50
53
53
54
52
53
51
54
53
54
52
52
52
50
50
53
55
55
53
51
51
51
52
55
54
54
51
50
50
51
53
54
52
53
52
56
56
56
54
53
53
51
50
51
52
53
54
54
53
52
51
51
52
50
51
51
53
53
52
52
51
51
52
53
53
52
51
51
51
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53
55
55
54
52
51
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50
50
50
51
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52
54
53
53
51
51
52
53
54
55
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53
53
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55
55
58
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56
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52
53
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55
57
59
61
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57
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65
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60
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59
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63
65
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64
62
62
61
62
61
61
61
62
63
62
62
62
62
62
62
62
61
62
63
64
67
67
65
61
59
62
63
63
62
62
62
64
66
66
64
63
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64
65
63
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67
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66
64
64
65
67

Answer 1

I used R software to solve this question.

R codes:

> x=scan('clipboard')
Read 328 items
> x
[1] 49 51 51 53 52 51 51 50 51 49 50 50 52 51 49 48 48 48 50 50 50 47 49 52 52
[26] 51 49 51 51 51 49 49 49 49 49 48 49 49 50 50 50 53 53 54 52 53 51 54 53 54
[51] 52 52 52 50 50 53 55 55 53 51 51 51 52 55 54 54 51 50 50 51 53 54 52 53 52
[76] 56 56 56 54 53 53 51 50 51 52 53 54 54 53 52 51 51 52 50 51 51 53 53 52 52
[101] 51 51 52 53 53 52 51 51 51 51 52 53 55 55 54 52 51 50 50 50 50 51 51 52 54
[126] 53 53 51 51 52 53 54 55 54 53 53 54 55 55 58 58 56 56 55 56 55 56 54 52 53
[151] 54 56 56 55 56 55 57 59 61 60 60 58 58 59 60 59 58 58 58 57 56 58 59 60 62
[176] 61 63 60 59 57 59 59 61 60 60 57 57 58 61 61 62 61 62 63 61 60 59 61 62 62
[201] 62 62 63 63 64 62 63 62 64 64 65 64 64 62 64 64 65 63 64 63 65 63 64 64 65
[226] 66 66 66 66 67 66 67 67 68 67 65 63 63 63 65 65 66 65 65 64 63 63 62 61 62
[251] 62 63 62 63 62 60 59 60 61 61 62 63 62 61 60 59 60 60 62 62 62 63 63 65 65
[276] 64 62 62 61 62 61 61 61 62 63 62 62 62 62 62 62 62 61 62 63 64 67 67 65 61
[301] 59 62 63 63 62 62 62 64 66 66 64 63 63 66 64 65 63 65 65 66 66 67 67 66 64
[326] 64 65 67
> chisq.test(x)

Chi-squared test for given probabilities

data: x
X-squared = 183.33, df = 327, p-value = 1

Hypothesis:

H₀: There is no significant difference between observed and expected values.

H₁: There is significant difference between observed and expected values.

Here p value is much greater than alpha=0.05, we accept null hypothesis and conclude that, There is no significant difference between observed and expected values.