Question
Is There a Significant Difference Between Men's and Women's Systolic Blood Pressures? project Goal: To explore two-sample confidence intervals and two-sample hypothesis testing for quantitative
Is There a Significant Difference Between Men's and Women's Systolic Blood Pressures?"
project Goal: To explore two-sample confidence intervals and two-sample hypothesis testing for quantitative data.
Directions Overview: You will explore a pair of datasets provided by your instructor and report on the procedures, results, and conclusions. In your report, be sure to use full sentences, and justify your answers using specific details or values as appropriate. The following template will guide you through this process.
The data is as follows:
Women's data:
Sample #1 | Sample #2 | Sample #3 | Sample #4 | Sample #5 | Sample #6 | Sample #7 | Sample #8 | Sample #9 | Sample #10 |
94 | 118 | 127 | 107 | 110 | 101 | 102 | 115 | 117 | 116 |
152 | 141 | 133 | 95 | 99 | 129 | 115 | 143 | 130 | 118 |
103 | 117 | 117 | 125 | 118 | 152 | 122 | 115 | 104 | 142 |
96 | 84 | 103 | 106 | 108 | 99 | 110 | 99 | 121 | 143 |
102 | 98 | 142 | 121 | 113 | 117 | 167 | 129 | 98 | 121 |
127 | 122 | 135 | 111 | 107 | 142 | 133 | 128 | 109 | 119 |
132 | 126 | 119 | 116 | 106 | 115 | 159 | 132 | 161 | 112 |
160 | 100 | 104 | 114 | 115 | 114 | 131 | 142 | 170 | 124 |
128 | 160 | 133 | 126 | 118 | 144 | 161 | 152 | 105 | 119 |
133 | 116 | 156 | 99 | 106 | 126 | 104 | 108 | 103 | 163 |
112 | 102 | 151 | 120 | 104 | 103 | 109 | 126 | 102 | 114 |
117 | 113 | 92 | 97 | 135 | 141 | 117 | 119 | 121 | 106 |
104 | 105 | 127 | 114 | 139 | 106 | 106 | 105 | 125 | 103 |
112 | 120 | 127 | 129 | 126 | 107 | 110 | 92 | 97 | 149 |
124 | 133 | 131 | 156 | 112 | 143 | 117 | 108 | 105 | 118 |
129 | 98 | 97 | 132 | 118 | 161 | 115 | 108 | 129 | 108 |
104 | 113 | 115 | 133 | 105 | 84 | 104 | 101 | 110 | 99 |
107 | 160 | 106 | 101 | 124 | 102 | 89 | 107 | 116 | 120 |
108 | 108 | 130 | 131 | 111 | 103 | 137 | 126 | 138 | 111 |
109 | 104 | 102 | 131 | 100 | 115 | 105 | 116 | 107 | 102 |
105 | 120 | 137 | 110 | 96 | 114 | 157 | 164 | 114 | 103 |
133 | 100 | 91 | 119 | 148 | 104 | 115 | 111 | 141 | 115 |
108 | 119 | 118 | 96 | 106 | 91 | 104 | 106 | 133 | 102 |
126 | 116 | 112 | 104 | 124 | 142 | 139 | 108 | 110 | 105 |
141 | 105 | 116 | 103 | 127 | 132 | 138 | 96 | 120 | 143 |
130 | 107 | 157 | 119 | 103 | 102 | 99 | 123 | 92 | 125 |
142 | 114 | 123 | 101 | 112 | 109 | 102 | 95 | 134 | 120 |
120 | 111 | 114 | 112 | 100 | 108 | 123 | 122 | 89 | 116 |
124 | 135 | 116 | 131 | 103 | 123 | 125 | 89 | 110 | 110 |
114 | 114 | 101 | 117 | 124 | 103 | 120 | 83 | 121 | 98 |
105 | 123 | 116 | 108 | 111 | 168 | 158 | 107 | 140 | 115 |
107 | 127 | 105 | 111 | 149 | 152 | 120 | 114 | 125 | 133 |
115 | 131 | 114 | 124 | 122 | 95 | 109 | 119 | 120 | 128 |
95 | 97 | 143 | 135 | 110 | 99 | 99 | 112 | 119 | 196 |
128 | 116 | 148 | 113 | 117 | 111 | 161 | 105 | 108 | 141 |
102 | 99 | 114 | 106 | 107 | 109 | 102 | 130 | 161 | 118 |
138 | 105 | 114 | 158 | 114 | 105 | 141 | 148 | 111 | 104 |
101 | 112 | 106 | 105 | 103 | 128 | 102 | 121 | 99 | 89 |
129 | 115 | 106 | 110 | 106 | 136 | 107 | 109 | 154 | 160 |
109 | 109 | 116 | 217 | 122 | 111 | 95 | 140 | 102 | 137 |
120 | 133 | 106 | 118 | 105 | 92 | 129 | 127 | 114 | 108 |
104 | 158 | 126 | 98 | 107 | 131 | 98 | 109 | 138 | 120 |
124 | 121 | 113 | 118 | 105 | 101 | 104 | 115 | 106 | 100 |
128 | 112 | 135 | 92 | 131 | 119 | 112 | 96 | 144 | 128 |
109 | 90 | 142 | 114 | 101 | 132 | 123 | 97 | 193 | 130 |
114 | 118 | 115 | 136 | 107 | 102 | 132 | 124 | 124 | 119 |
97 | 138 | 102 | 95 | 113 | 153 | 116 | 89 | 166 | 101 |
86 | 103 | 103 | 116 | 124 | 150 | 117 | 113 | 100 | 106 |
134 | 114 | 112 | 105 | 133 | 133 | 134 | 111 | 113 | 113 |
102 | 124 | 114 | 109 | 120 | 123 | 114 | 119 | 96 | 116 |
103 | 120 | 100 | 112 | 100 | 112 | 104 | 104 | 138 | 108 |
138 | 113 | 107 | 136 | 163 | 129 | 124 | 116 | 109 | 101 |
112 | 160 | 111 | 112 | 129 | 117 | 105 | 94 | 136 | 97 |
113 | 113 | 129 | 113 | 137 | 105 | 100 | 160 | 110 | 128 |
132 | 158 | 141 | 196 | 97 | 121 | 152 | 119 | 120 | 99 |
112 | 101 | 136 | 121 | 123 | 160 | 105 | 142 | 160 | 104 |
96 | 133 | 113 | 86 | 123 | 112 | 145 | 146 | 132 | 156 |
102 | 117 | 100 | 114 | 142 | 153 | 101 | 108 | 117 | 103 |
100 | 121 | 112 | 137 | 102 | 113 | 109 | 101 | 121 | 105 |
105 | 122 | 116 | 91 | 158 | 107 | 112 | 124 | 108 | 108 |
Men's data:
Sample #11 | Sample #12 | Sample #13 | Sample #14 | Sample #15 | Sample #16 | Sample #17 | Sample #18 | Sample #19 | Sample #20 |
99 | 126 | 106 | 113 | 139 | 146 | 114 | 123 | 153 | 111 |
115 | 148 | 139 | 121 | 109 | 130 | 158 | 120 | 115 | 121 |
114 | 119 | 122 | 119 | 105 | 100 | 132 | 114 | 119 | 127 |
119 | 123 | 119 | 108 | 111 | 138 | 128 | 105 | 136 | 137 |
144 | 154 | 115 | 108 | 121 | 131 | 120 | 122 | 146 | 158 |
130 | 111 | 121 | 174 | 120 | 126 | 120 | 122 | 131 | 113 |
105 | 130 | 112 | 132 | 116 | 98 | 110 | 145 | 105 | 131 |
128 | 118 | 119 | 105 | 122 | 125 | 111 | 115 | 107 | 111 |
117 | 134 | 103 | 104 | 141 | 126 | 121 | 167 | 126 | 111 |
118 | 107 | 114 | 114 | 153 | 121 | 139 | 125 | 116 | 129 |
115 | 109 | 125 | 131 | 103 | 123 | 118 | 118 | 122 | 123 |
144 | 136 | 134 | 119 | 113 | 100 | 107 | 111 | 129 | 121 |
165 | 104 | 121 | 149 | 134 | 120 | 122 | 171 | 143 | 141 |
118 | 120 | 130 | 119 | 119 | 130 | 130 | 108 | 138 | 111 |
116 | 124 | 117 | 113 | 137 | 122 | 114 | 136 | 129 | 147 |
110 | 120 | 102 | 108 | 130 | 107 | 128 | 128 | 131 | 122 |
119 | 110 | 108 | 117 | 132 | 122 | 111 | 120 | 93 | 137 |
116 | 112 | 120 | 118 | 143 | 136 | 111 | 133 | 108 | 123 |
114 | 152 | 126 | 100 | 125 | 113 | 121 | 130 | 129 | 122 |
118 | 120 | 115 | 107 | 111 | 106 | 123 | 122 | 99 | 136 |
124 | 118 | 120 | 111 | 135 | 136 | 110 | 109 | 110 | 115 |
149 | 122 | 109 | 124 | 131 | 102 | 125 | 124 | 120 | 129 |
113 | 147 | 127 | 130 | 130 | 113 | 126 | 103 | 115 | 140 |
112 | 160 | 124 | 102 | 108 | 118 | 123 | 111 | 142 | 119 |
135 | 102 | 119 | 109 | 159 | 91 | 110 | 113 | 116 | 98 |
141 | 125 | 121 | 119 | 118 | 131 | 99 | 111 | 112 | 109 |
145 | 120 | 123 | 125 | 132 | 159 | 114 | 95 | 136 | 119 |
130 | 126 | 119 | 140 | 171 | 180 | 159 | 145 | 112 | 139 |
134 | 121 | 127 | 107 | 93 | 120 | 116 | 109 | 96 | 142 |
126 | 119 | 125 | 121 | 125 | 115 | 109 | 119 | 114 | 117 |
120 | 112 | 113 | 128 | 106 | 130 | 141 | 102 | 156 | 114 |
116 | 140 | 128 | 125 | 112 | 126 | 137 | 113 | 114 | 114 |
113 | 116 | 130 | 118 | 111 | 107 | 121 | 139 | 108 | 120 |
122 | 129 | 121 | 191 | 118 | 138 | 113 | 101 | 129 | 148 |
141 | 110 | 103 | 123 | 119 | 142 | 128 | 127 | 105 | 114 |
124 | 137 | 139 | 145 | 100 | 138 | 126 | 137 | 101 | 88 |
159 | 106 | 119 | 138 | 118 | 120 | 133 | 161 | 137 | 93 |
133 | 141 | 114 | 111 | 95 | 116 | 146 | 125 | 111 | 126 |
120 | 113 | 165 | 105 | 112 | 122 | 107 | 105 | 122 | 113 |
121 | 119 | 121 | 130 | 139 | 112 | 115 | 160 | 126 | 147 |
125 | 116 | 109 | 98 | 125 | 135 | 137 | 149 | 116 | 103 |
122 | 119 | 111 | 111 | 117 | 128 | 107 | 103 | 102 | 135 |
118 | 137 | 129 | 133 | 107 | 121 | 111 | 112 | 150 | 110 |
131 | 118 | 122 | 108 | 141 | 139 | 88 | 116 | 132 | 137 |
130 | 137 | 121 | 142 | 130 | 119 | 108 | 115 | 114 | 113 |
96 | 114 | 125 | 137 | 109 | 156 | 129 | 123 | 112 | 134 |
129 | 124 | 128 | 112 | 112 | 109 | 127 | 115 | 129 | 120 |
114 | 133 | 138 | 135 | 124 | 141 | 125 | 130 | 120 | 109 |
124 | 122 | 134 | 120 | 114 | 109 | 153 | 125 | 141 | 149 |
125 | 164 | 151 | 129 | 112 | 110 | 113 | 132 | 104 | 107 |
126 | 179 | 131 | 102 | 134 | 98 | 119 | 110 | 131 | 111 |
146 | 113 | 131 | 122 | 120 | 126 | 104 | 120 | 119 | 125 |
139 | 96 | 116 | 124 | 114 | 100 | 125 | 111 | 110 | 130 |
110 | 116 | 132 | 140 | 132 | 125 | 121 | 138 | 126 | 120 |
143 | 112 | 116 | 118 | 112 | 133 | 116 | 107 | 126 | 147 |
138 | 122 | 101 | 129 | 122 | 154 | 193 | 118 | 122 | 126 |
132 | 124 | 129 | 123 | 125 | 160 | 119 | 142 | 113 | 119 |
100 | 116 | 117 | 148 | 121 | 118 | 130 | 126 | 111 | 121 |
102 | 120 | 128 | 153 | 126 | 110 | 132 | 103 | 161 | 118 |
134 | 119 | 95 | 131 | 124 | 105 | 143 | 108 | 118 | 117 |
Natural order | Randomized order | ||
First dataset (women's systolic BP in mmHg) | Second dataset (men's systolic BP in mmHg) | First dataset (women's systolic BP in mmHg) | Second dataset (men's systolic BP in mmHg) |
Sample #1 | Sample #11 | Sample #7 | Sample #17 |
Sample #2 | Sample #11 | Sample #2 | Sample #11 |
Sample #3 | Sample #11 | Sample #2 | Sample #20 |
Sample #4 | Sample #11 | Sample #8 | Sample #15 |
Sample #5 | Sample #11 | Sample #5 | Sample #19 |
Sample #6 | Sample #11 | Sample #2 | Sample #15 |
Sample #7 | Sample #11 | Sample #2 | Sample #19 |
Sample #8 | Sample #11 | Sample #7 | Sample #18 |
Sample #9 | Sample #11 | Sample #7 | Sample #20 |
Sample #10 | Sample #11 | Sample #7 | Sample #19 |
Sample #1 | Sample #12 | Sample #4 | Sample #12 |
Sample #2 | Sample #12 | Sample #8 | Sample #17 |
Sample #3 | Sample #12 | Sample #8 | Sample #13 |
Sample #4 | Sample #12 | Sample #6 | Sample #18 |
Sample #5 | Sample #12 | Sample #4 | Sample #20 |
Sample #6 | Sample #12 | Sample #4 | Sample #15 |
Sample #7 | Sample #12 | Sample #1 | Sample #12 |
Sample #8 | Sample #12 | Sample #6 | Sample #17 |
Sample #9 | Sample #12 | Sample #10 | Sample #12 |
Sample #10 | Sample #12 | Sample #3 | Sample #14 |
Sample #1 | Sample #13 | Sample #10 | Sample #16 |
Sample #2 | Sample #13 | Sample #10 | Sample #17 |
Sample #3 | Sample #13 | Sample #6 | Sample #12 |
Sample #4 | Sample #13 | Sample #6 | Sample #16 |
Sample #5 | Sample #13 | Sample #1 | Sample #19 |
Sample #6 | Sample #13 | Sample #1 | Sample #13 |
Sample #7 | Sample #13 | Sample #4 | Sample #19 |
Sample #8 | Sample #13 | Sample #9 | Sample #11 |
Sample #9 | Sample #13 | Sample #9 | Sample #17 |
Sample #10 | Sample #13 | Sample #6 | Sample #20 |
Sample #1 | Sample #14 | Sample #10 | Sample #19 |
Sample #2 | Sample #14 | Sample #3 | Sample #15 |
Sample #3 | Sample #14 | Sample #2 | Sample #13 |
Sample #4 | Sample #14 | Sample #6 | Sample #19 |
Sample #5 | Sample #14 | Sample #2 | Sample #14 |
Sample #6 | Sample #14 | Sample #8 | Sample #20 |
Sample #7 | Sample #14 | Sample #6 | Sample #15 |
Sample #8 | Sample #14 | Sample #1 | Sample #15 |
Sample #9 | Sample #14 | Sample #1 | Sample #14 |
Sample #10 | Sample #14 | Sample #1 | Sample #17 |
Sample #1 | Sample #15 | Sample #2 | Sample #18 |
Sample #2 | Sample #15 | Sample #7 | Sample #15 |
Sample #3 | Sample #15 | Sample #4 | Sample #13 |
Sample #4 | Sample #15 | Sample #10 | Sample #11 |
Sample #5 | Sample #15 | Sample #8 | Sample #19 |
Sample #6 | Sample #15 | Sample #3 | Sample #13 |
Sample #7 | Sample #15 | Sample #9 | Sample #20 |
Sample #8 | Sample #15 | Sample #5 | Sample #16 |
Sample #9 | Sample #15 | Sample #1 | Sample #11 |
Sample #10 | Sample #15 | Sample #1 | Sample #16 |
Sample #1 | Sample #16 | Sample #8 | Sample #18 |
Sample #2 | Sample #16 | Sample #4 | Sample #18 |
Sample #3 | Sample #16 | Sample #4 | Sample #11 |
Sample #4 | Sample #16 | Sample #5 | Sample #14 |
Sample #5 | Sample #16 | Sample #9 | Sample #15 |
Sample #6 | Sample #16 | Sample #3 | Sample #11 |
Sample #7 | Sample #16 | Sample #2 | Sample #16 |
Sample #8 | Sample #16 | Sample #5 | Sample #11 |
Sample #9 | Sample #16 | Sample #9 | Sample #12 |
Sample #10 | Sample #16 | Sample #10 | Sample #13 |
Sample #1 | Sample #17 | Sample #8 | Sample #16 |
Sample #2 | Sample #17 | Sample #5 | Sample #20 |
Sample #3 | Sample #17 | Sample #3 | Sample #17 |
Sample #4 | Sample #17 | Sample #10 | Sample #20 |
Sample #5 | Sample #17 | Sample #9 | Sample #16 |
Sample #6 | Sample #17 | Sample #5 | Sample #12 |
Sample #7 | Sample #17 | Sample #10 | Sample #15 |
Sample #8 | Sample #17 | Sample #4 | Sample #14 |
Sample #9 | Sample #17 | Sample #8 | Sample #14 |
Sample #10 | Sample #17 | Sample #7 | Sample #12 |
Sample #1 | Sample #18 | Sample #6 | Sample #11 |
Sample #2 | Sample #18 | Sample #10 | Sample #14 |
Sample #3 | Sample #18 | Sample #7 | Sample #16 |
Sample #4 | Sample #18 | Sample #8 | Sample #11 |
Sample #5 | Sample #18 | Sample #2 | Sample #17 |
Sample #6 | Sample #18 | Sample #3 | Sample #19 |
Sample #7 | Sample #18 | Sample #7 | Sample #14 |
Sample #8 | Sample #18 | Sample #5 | Sample #17 |
Sample #9 | Sample #18 | Sample #1 | Sample #20 |
Sample #10 | Sample #18 | Sample #9 | Sample #19 |
Sample #1 | Sample #19 | Sample #3 | Sample #12 |
Sample #2 | Sample #19 | Sample #9 | Sample #13 |
Sample #3 | Sample #19 | Sample #1 | Sample #18 |
Sample #4 | Sample #19 | Sample #6 | Sample #13 |
Sample #5 | Sample #19 | Sample #6 | Sample #14 |
Sample #6 | Sample #19 | Sample #9 | Sample #14 |
Sample #7 | Sample #19 | Sample #5 | Sample #18 |
Sample #8 | Sample #19 | Sample #5 | Sample #15 |
Sample #9 | Sample #19 | Sample #4 | Sample #17 |
Sample #10 | Sample #19 | Sample #7 | Sample #13 |
Sample #1 | Sample #20 | Sample #4 | Sample #16 |
Sample #2 | Sample #20 | Sample #3 | Sample #20 |
Sample #3 | Sample #20 | Sample #3 | Sample #16 |
Sample #4 | Sample #20 | Sample #9 | Sample #18 |
Sample #5 | Sample #20 | Sample #2 | Sample #12 |
Sample #6 | Sample #20 | Sample #7 | Sample #11 |
Sample #7 | Sample #20 | Sample #8 | Sample #12 |
Sample #8 | Sample #20 | Sample #10 | Sample #18 |
Sample #9 | Sample #20 | Sample #3 | Sample #18 |
Sample #10 | Sample #20 | Sample #5 | Sample #13 |
For Questions 1 and 2, you will review the quantitative datasets that you were assigned.
- Referring to the data provided to you by your instructor:
- The data you were assigned are a subset of the data collected as part of the National Health and Nutrition Examination Survey (NHANES) in 2011-2012. Here is a link to a website that explains how the data were collected. Do you believe these datasets are representative of the population? Give your answer and support it in sentences.
- Use technology to answer the following questions. (Hint: Consider using the Describing and Exploring Quantitative Variables ShinyApphttps://dcmathpathways.shinyapps.io/EDA_quantitative/)
- Provide a screen clip of the Descriptive Statistics for both of your datasets. Be sure to adjust the group names/labels so they describe your data.
- Provide screen clips of the side-by-side boxplots AND side-by-side histograms. Label each graph to show which is which.
- In sentences, describe in detail the distribution of each dataset. (Hint: Refer to In-Class Activity 3D for the four main characteristics we use to describe distributions.)
For Questions 3 through 6, you will set up, calculate, and analyze inferential statistics (confidence interval and hypothesis test) for the two datasets you were assigned.
- Are your two datasets independent or dependent? Give your answer and support it in a couple sentences.
- Use technology to construct and interpret the 95% confidence interval. (Hint: Consider using the Compare Two Population Means ShinyApphttps://dcmathpathways.shinyapps.io/2sample_mean/)
- What point estimate can we use to construct a confidence interval for the difference between the two assigned data sets? Include appropriate units.
- What is the margin of error? Include appropriate units.
- What is the 95% confidence interval? Use interval notation.
- In a couple sentences, interpret the confidence interval in context of the application, using appropriate units.
- Develop a hypothesis about your population means.
- Make a sentence describing your developed hypothesis about the two population means.(Example: I hypothesize that the mean household income in 2020 was higher than the mean household income in 2016.)
- Explain what the symbols and OR represent in context.
- the null hypothesis in symbols.
- the alternative hypothesis in symbols.
- Is your hypothesis test one-tailed or two-tailed?
- Conduct the hypothesis test at a level of significance 5%, . (Hint: Consider using the Compare Two Population Means ShinyApp https://dcmathpathways.shinyapps.io/2sample_mean/)
- What is the test statistic?
- What is the p-value?
- What is the conclusion about the null hypothesis?
- In a couple sentences, make a conclusion of the hypothesis test in context of the application, using correct units.
For Question 7, make a Final Report that summarizes and builds upon all the work from Questions 1 through 6.
- Make a Final Report for this project. This is a cohesive report, not a series of responses to questions. Use the following guidelines to structure the report:
- Introduction: Set the stage for the report by providing an overview of the two assigned datasets. Include a summary of the analysis from Questions 1 & 2.
- Confidence Interval Results: Summarize the results from the research and discuss the findings of your confidence interval. Incorporate the findings from Question 4.
- Hypothesis Test Results: Discuss the procedure, results, and conclusion of the hypothesis test. Incorporate the findings from Questions 5 & 6.
- Conclusion: Based on the project results, do you believe there is a significant difference between men's and women's systolic blood pressures? Reflect on the results of the data analysis, confidence interval, and hypothesis test. Comment on the alignment between the confidence interval and hypothesis test results. Discuss any results that were surprising, interesting, or confirmed your expectations. Include at least one good statistical question related to your research you would like to investigate further. Include reflections about the project that would add insight.
Questions 8 and 9 give you the opportunity to use statistics to explore your own interests.
- Make a good statistical question about a topic that interests you, personally or professionally, that would require a study of two means for quantitative data.
- Design a method for collecting sample data that would answer the statistical question from Question #8.
- Explain how you would acquire the data. Be specific.
- Explain why your data collection method would be an observational study or an experiment.
- Would your two datasets be independent or dependent? Give your answer and support it in sentences.
Thank you if you even come across this question and attempt to help:)
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