The z Test on Independent Proportions: Write a research question for a test on p
ID: 3357754 • Letter: T
Question
The z Test on Independent Proportions: Write a research question for a test on proportions. Include the null and alternative hypotheses (2 points) Open the Howell data setPreview the documentView in a new window Using the hypothesis testing procedure we learned in class, select any appropriate independent and any appropriate dependent variable from the Howell data set. Perform an independent test on proportions and make a correct conclusion (2 points). Report the correct decision regarding the null hypothesis (2 point) Based on your analysis, report the results in 1-2 paragraphs using correct APA format (1 point). For example, “Residents who were exposed to contaminated water had significantly more birth defects (0.04) than residents who were not (0.02); z=2.35, p <0.05.” https://scccd.instructure.com/courses/20230/files/1001663/download?verifier=xN055fwgx4cPAKUg0ZYMPipuul37N0Rnumz8wsac&wrap=1
GENDER REPEAT ENGL ENGG SOCPROB DROPOUT ADDSC IQ GPA 0 0 2 3 0 0 41.33333 111 2.6 0 0 2 3 0 0 47.33333 102 2.75 0 0 2 4 0 0 47.66667 108 4 0 0 2 2 0 0 61.33333 109 2.25 0 0 2 3 0 0 35.33333 118 3 0 1 2 2 0 1 61.33333 79 1.67 0 0 2 2 1 1 59.66667 88 2.25 0 0 2 2 0 0 58 84 3 0 0 2 4 0 0 37.66667 131 3.75 1 0 2 3 0 0 56 104 2.67 0 0 2 3 0 0 73.66667 83 2.75 0 0 2 2 0 0 47.33333 84 2 0 0 2 3 0 0 48.33333 85 2.75 0 0 2 2 0 0 56 110 2.5 1 0 2 4 0 0 51.66667 101 3.25 1 0 2 4 0 0 48.33333 93 3.25 1 0 2 4 0 0 44.33333 128 3.3 1 0 2 3 0 0 56.66667 84 2.75 1 0 2 4 0 0 37.33333 127 3.75 1 0 2 3 0 0 40.33333 106 2.75 0 0 2 3 0 0 35.33333 137 3 0 1 2 2 0 0 68.33333 82 1.75 0 0 2 2 0 0 48.66667 107 2 0 0 2 2 0 0 51.33333 95 2.75 0 0 2 3 0 0 64 97 2.67 0 0 2 2 0 0 72.66667 93 2 0 1 2 2 0 0 61 81 2 1 0 2 2 0 0 63.66667 89 1.67 1 0 2 4 0 0 60 111 3 1 0 2 1 0 1 69.33333 95 1.5 1 0 1 4 0 0 38.33333 106 3.75 1 0 2 1 0 0 68 83 0.67 0 0 2 2 1 0 65 81 1.5 1 0 1 4 0 0 44 115 4 1 0 1 3 0 0 48 112 3 1 0 2 3 0 0 57.66667 92 2.33 1 0 1 2 0 0 59 85 1.75 1 0 2 2 0 0 55 95 3 1 0 2 4 0 0 43.33333 115 3.75 1 0 2 3 0 1 60 93 1.25 1 0 2 3 0 0 24.66667 129 3.2 1 0 1 3 1 0 60.33333 96 3 1 0 2 3 0 0 37.33333 114 3.5 0 0 2 2 0 0 51 105 1.75 0 0 2 1 0 0 67.33333 83 1 0 0 3 3 0 0 42.33333 120 3 0 0 2 1 0 0 56.33333 88 1 0 0 2 3 0 0 53 93 2.5 0 1 2 1 1 1 76.33333 86 1 0 0 2 3 0 0 65.33333 106 2.75 0 0 2 2 0 0 55.33333 109 1.33 0 0 2 1 0 1 67.66667 55 1.67 0 0 2 2 0 0 42.66667 111 2.25 0 0 2 2 0 0 58.66667 105 1.75 0 0 2 2 0 0 54 103 1.75 0 0 2 3 0 0 53.66667 101 3 0 0 1 3 0 0 51.66667 101 3 0 0 2 2 0 1 59 90 2.67 0 1 2 3 0 0 56.33333 95 3 0 1 2 1 0 0 65 108 1.25 0 0 1 3 1 0 55.33333 95 2.25 0 0 2 1 0 0 68 98 1 0 0 3 3 1 1 53.66667 82 0.25 1 0 1 3 0 0 45 100 3 1 0 2 3 0 0 49.66667 100 2.4 1 0 3 3 0 0 65.33333 85 2.5 1 0 1 4 0 0 41 105.5 3.75 1 0 2 2 0 1 55.33333 107 0.6 1 0 1 4 0 0 33.66667 108.5 3.5 1 0 2 4 0 0 37 122 4 1 0 2 2 0 0 54 105 2.6 1 0 1 2 0 0 35 113.5 3.75 1 0 2 3 0 0 51.66667 95 3.75 1 0 2 1 0 0 48 124.5 1 1 0 1 4 0 0 27.33333 125.5 3.5 1 0 2 3 0 0 50 120 3.5 1 0 3 2 0 0 57 106 3 1 0 3 3 0 1 55.33333 96 2.5 1 0 2 3 0 0 36.66667 108 2.5 1 0 3 4 0 0 52 92 3 0 0 3 3 0 0 41.66667 104 3 0 0 2 2 0 0 51.66667 99 2.25 0 0 2 2 0 0 50.66667 103 1.6 0 0 3 2 1 0 57.66667 75 1 0 1 3 3 0 0 47.66667 90.5 2.25 0 0 2 2 1 0 76.66667 96 1 0 0 3 3 0 0 39.66667 108 2.5 0 0 2 3 0 0 52.66667 86 2.75 0 0 3 2 0 0 55.66667 97.5 0.75 0 0 2 2 0 0 47.66667 99 1.3 0 0 3 2 1 1 64 92 1.25 0 0 3 1 0 0 64.33333 95 1.25 0 0 3 3 0 0 69 88 1.5 0 0 2 2 0 0 44.33333 111 3 0 0 2 1 0 0 53.33333 103 2 0 0 2 2 0 0 55 107 2 0 0 1 2 0 0 41.66667 118 2.5 0 0 2 2 0 0 57.33333 116 2.1 0 0 3 3 0 0 52.66667 84 2.5 0 1 3 3 0 1 62.33333 80 2.67 0 0 3 3 0 0 69.66667 79 2 0 0 3 3 0 0 61.33333 78 2.25 0 0 3 3 0 0 43.66667 106 2.25 0 1 2 3 0 0 49.66667 91.5 2.75 0 0 2 2 0 0 49 97 1.5 0 0 2 1 0 0 54.33333 112 1.6 1 0 3 3 0 0 50.33333 109 2.75 0 0 3 2 0 0 75.33333 102 2.25 0 0 3 3 0 0 58 108 2.5 1 0 2 2 0 0 49 102 2.3 1 0 2 2 0 0 41 101.5 1.5 1 0 2 3 0 0 46.66667 105 2.2 0 0 2 3 0 0 51.33333 91 3.75 1 0 2 4 0 0 46.66667 93.5 3 1 0 1 4 0 0 46.66667 110.5 4 1 0 2 4 0 0 41 118 4 1 0 2 3 0 0 44.33333 108 2.4 1 0 2 3 0 0 47.33333 110 2.75 1 0 2 4 0 0 53.33333 106.5 3 1 0 2 4 0 0 47.33333 96 2.75 0 0 2 3 0 0 51 106 2.66 0 1 2 1 0 0 60.33333 97 1.5 0 0 2 2 0 0 53.66667 117 2.4 0 0 2 3 0 0 51.66667 109 1.5 0 0 2 2 0 0 53.33333 98 2.2 0 0 2 2 0 0 60.66667 117 2.3 1 0 2 2 0 0 51 102 1.4 1 0 2 3 0 0 46 107 3 1 0 2 2 0 0 53.33333 107 1.8 1 0 1 3 0 0 42.66667 105 3.75 0 0 2 3 1 0 69 92 3.25 0 0 2 2 0 0 69 104 1.75 0 0 2 3 1 0 68.33333 104 2.33 0 0 1 3 0 0 36.66667 125 3.5 0 0 2 2 0 0 41 113.5 2.56 0 0 2 2 1 0 60 97.5 2.5 0 0 2 2 0 0 59 103 3.25 0 0 3 2 0 0 34 129 3.25 0 0 2 3 1 0 68.33333 100.5 2.5 0 0 3 2 1 0 62 90 2 0 0 2 1 1 1 57.33333 107 1.75 1 0 3 3 0 0 53.33333 89.5 2 1 0 2 4 0 0 51.66667 117 3.5 1 0 2 3 0 0 46.66667 115 2.75 1 0 1 2 0 0 41.33333 103 2.5 1 0 1 3 0 0 38.66667 125.5 3.5 1 0 2 3 0 0 54.33333 117.5 3 1 0 2 2 0 0 61 111 2.7 1 0 2 2 0 0 53.66667 112 2 1 0 1 3 0 0 34 123 2.7 1 0 2 3 0 0 40 110.5 3.75 1 0 2 2 0 0 53.66667 105.5 2.25 0 0 1 3 0 0 40.33333 119.5 2.5 0 0 2 2 0 0 60.66667 108 1.7 0 0 3 1 0 0 71 97.5 1 0 0 2 2 0 0 54.66667 88 1.69 0 0 2 3 0 0 51.66667 109.5 3.3 0 0 2 2 0 0 64 104 3.25 0 0 2 2 0 0 41 114 2.25 0 0 2 1 1 0 65.66667 99.5 1.67 0 0 2 2 0 0 55 106.5 2.67 0 0 2 2 0 0 56 106 2 0 0 3 2 0 0 58 94.5 2 0 0 2 2 0 1 48.33333 111.5 1.75 0 0 3 1 1 1 67 99 0.67 1 1 1 3 0 0 38 116 3.5 1 0 2 3 1 0 49.66667 118 3 1 0 2 0 1 0 61 91.5 1 1 0 2 2 0 0 49.33333 116 2.25 1 0 2 3 0 0 52.33333 105.5 3 1 0 1 3 0 0 40 124.5 3.75 1 0 2 2 0 0 56.33333 93 2.25 0 0 1 1 0 0 58.66667 95.5 1.5 1 0 2 3 0 0 61.66667 108 3 1 0 2 2 0 0 50 104 3.06 1 0 1 2 0 0 43 112 3 1 0 2 2 0 1 63.33333 95 2.43 0 1 3 2 0 0 74 93 2 0 0 1 3 0 0 45 119 3.75 0 1 3 2 0 0 63 88 2.25 0 1 3 0 1 1 66.66667 91 0.75 0 0 2 1 1 0 62 85.5 1.33 1 0 1 2 0 0 39 111 2 0 1 2 4 1 0 66 94 3.25 1 0 2 3 0 0 35 102.5 2.5 1 0 2 1 1 1 53 103 1.33 1 0 2 3 0 0 47 105.5 2.7 1 0 1 3 0 0 39.66667 123.5 3.5 1 1 2 2 0 0 54 102.5 2.75 1 0 2 3 0 0 57.33333 113 2.67 1 0 1 2 0 0 44.66667 119 3 0 0 2 2 0 0 40.5 105 1 0 0 2 2 0 0 53 99 1.83 1 0 2 3 0 0 51.5 101 3 1 0 3 3 0 0 25.5 116 3.75 0 1 2 1 0 0 53 91 1 1 0 2 3 0 0 48 100 2.5 1 0 2 3 0 0 52.5 114 2.4 0 1 2 1 0 0 71.5 98.5 0.81 0 0 2 1 0 0 67 94 2.33Explanation / Answer
Solution:
Here, we want to analyze the research question whether the research study included the same proportion of the male and female. For checking or testing this hypothesis we have to use Z test for population proportions. The null and alternative hypotheses for this test are summarized as below:
Null hypothesis: H0: There is no any significant difference in the proportions of the male and female.
Alternative hypothesis: Ha: There is a significant difference in the proportions of the male and female.
Symbolically, the null and alternative hypotheses are given as below:
H0: p1 = p2 Versus Ha: p1 p2
This is a two tailed test.
We assume 5% level of significance for this test.
= 0.05
The test statistic formula for this test is given as below:
Z = (P1 – P2) / sqrt[(P1(1 – P1)/N1)+(P2*(1 – P2)/N2)]
From the given data, we have
Number of male = X1 = 112
Sample size = N1 = 200
Sample proportion = P1 = X1/N2 = 112/200 = 0.56
Number of female = X2 = 88
Sample size = N2 = 200
Sample proportion = P2 = X2/N2 = 88/200 = 0.44
Difference in two proportions = (P1 – P2) = 0.56 – 0.44 = 0.12
Standard error = sqrt[(P1(1 – P1)/N1)+(P2*(1 – P2)/N2)]
Standard error = sqrt[(0.56*(1 – 0.56)/200)+(0.44*(1 – 0.44)/200)]
Standard error = 0.049638695
Z = (P1 – P2) / sqrt[(P1(1 – P1)/N1)+(P2*(1 – P2)/N2)]
Z = 0.12/ 0.049638695
Z = 2.417468892
P-value = 0.01562887 (by using z-table or excel)
P-value < = 0.05
So, we reject the null hypothesis that there is no any significant difference in the proportions of the male and female.
There is insufficient evidence to conclude that the proportions of male and female included in the research study are not same.
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