{"id":5460,"date":"2022-08-30T19:48:49","date_gmt":"2022-08-30T19:48:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5460"},"modified":"2022-08-30T19:48:50","modified_gmt":"2022-08-30T19:48:50","slug":"14b-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/14b-preview\/","title":{"raw":"14B Preview","rendered":"14B Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to make connections between values\u00a0 presented in an ANOVA table and describe the shape of the F Distribution. You will also\u00a0 need to understand how the P-value is represented by an area under an F Distribution\u00a0 curve and describe how the F-statistic is used in hypothesis testing for a one-way\u00a0 ANOVA. Finally, you will need to use the P-value to reach a conclusion.\r\n\r\nSuppose a researcher wants to investigate the effect of the amount of fertilizer on the\u00a0 height of a common houseplant. More specifically, the researcher is interested in\u00a0 determining if there is a difference in the mean height of plants between those receiving\u00a0 one of following three different fertilizer levels: high, medium, and low.\r\n\r\nThe following data are the simulated results of this controlled experiment. (Note that this\u00a0 small dataset is used introduce the concept and make calculations easier. When\u00a0 conducting an ANOVA, larger sample sizes are usually needed to meet assumptions.)\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Fertilizer Level<\/td>\r\nHeight of Plant (inches)<\/td>\r\n<\/tr>\r\n
Low<\/td>\r\n23.2, 20.9, 21.5, 25.3<\/td>\r\n<\/tr>\r\n
Medium<\/td>\r\n24.6, 27.7, 22.5, 30.1<\/td>\r\n<\/tr>\r\n
High<\/td>\r\n29.2, 30.2, 31.1, 33.6<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nAs we saw in the previous in-class activity, conducting a one-way ANOVA involves\u00a0 comparing the variation within each of the groups to the variation between each of the\u00a0 groups. When the variation between each of the groups is significantly larger than the\u00a0 variation within each of the groups, we might conclude that there is a statistically significant difference among the means.\r\n\r\nIn an ANOVA table, the calculation illustrating the total variation within the groups of\u00a0 interest is known as the error sum of squares (SSError). The calculation illustrating\u00a0 the total variation between the groups is known as the group sum of squares (SSGroup).\r\n\r\nTwo other essential columns found in an ANOVA table are the degrees of freedom (df) and the mean square.\r\n\r\nThe following table illustrates how these values are calculated for each of the given\u00a0 sources: Group or Error (i.e., between and within).\r\n\r\nWhen calculating these values, it is important to know that [latex]k[\/latex] represents the number of\u00a0 groups being considered and [latex]N[\/latex] represents the total number of data values among all\u00a0 groups.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/td>\r\nDegrees of Freedom (df)<\/td>\r\nSum of\u00a0\u00a0Squares<\/td>\r\nMean\u00a0\u00a0Square<\/td>\r\nF-Statistic<\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n[latex]k-1[\/latex]\r\n\r\n(The number of groups\u00a0 minus 1)<\/td>\r\nSSGroup<\/td>\r\nSSGroup\r\n\r\n[latex]k-1[\/latex]<\/td>\r\nMSGroup\r\n\r\nMSError<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n[latex]N-k[\/latex]\r\n\r\n(The total number of data\u00a0 points minus the number of\u00a0 groups)<\/td>\r\nSSError<\/td>\r\nSSError\r\n\r\n[latex]N-k[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n[latex]N-1[\/latex]\r\n\r\n(The total number of data\u00a0 points minus 1)<\/td>\r\nSSGroup +\u00a0 SSError<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n

Question 1<\/h3>\r\n
1) Given the information in the previous table, let\u2019s calculate the degrees of freedom\u00a0 associated with the Group and Error sources for the fertilizer and plant height\u00a0 scenario.<\/div>\r\nPart A: In the fertilizer and plant height scenario, what is the value for \ufffd (i.e., the\u00a0 number of groups)?\r\n\r\nPart B: In the fertilizer and plant height scenario, what is the value for \ufffd (i.e., the\u00a0 total number of data values in the experiment)?\r\n\r\nPart C: Given your previous responses, complete the Degrees of Freedom column\u00a0 for the fertilizer and plant height scenario in the following table.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/td>\r\nDegrees of\r\n\r\nFreedom (df)<\/td>\r\n<\/tr>\r\n
Group<\/td>\r\nk \u2212 1 =<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\nN \u2212 k =<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\nN \u2212 1 =<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\nWhen performing a formal hypothesis test for a one-way ANOVA, the mean square\u00a0 values are used to calculate the value of our test statistic; thus, they impact the P-value\u00a0 we get.\u00a0\u00a0<\/span>\r\n\r\n<\/div>\r\nAs noted in the previous table, the mean square for error and mean square for group are calculated by taking each of the sum of square values and dividing them by the\u00a0 degrees of freedom associated with the respective source (i.e., Group or Error).\r\n\r\n[latex]Mean\\;Square\\;for\\;Error\\;(MSError)=\\frac{Error\\;sum\\;of\\;squares}{degrees\\;of\\;freedom\\;(Error)}=\\frac{SSE}{N-k}[\/latex]\r\n\r\n[latex]Mean\\;Square\\;for\\;Group\\;(MSGroup)=\\frac{Group\\;sum\\;of\\;squares}{degrees\\;of\\;freedom\\;(Group)}=\\frac{SSG}{k-1}[\/latex]\r\n
\r\n

Question 2<\/h3>\r\n2) We are given the sum of squares and degrees of freedom for the fertilizer and plant\u00a0 height scenario. Use these values to calculate the mean square for error and mean\u00a0 square for group. Enter the values in the following table.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/td>\r\nDegrees of\r\n\r\nFreedom (df)<\/td>\r\nSum of Squares<\/td>\r\nMean Square<\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n2<\/td>\r\n55.9134<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n9<\/td>\r\n140.0108<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n11<\/td>\r\n195.9242<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
\r\n

Question 3<\/h3>\r\n3) The test statistic that we use to complete the appropriate hypothesis test for a one way ANOVA is calculated with the ratio below:\r\n\r\nF-Statistic = MSGroup\r\n\r\nMSError = Variation BETWEEN groups\r\n\r\nVariation WITHIN groups\r\n\r\nUse the MSGroup and MSError values you calculated to find the F-statistic for this\u00a0 situation:\r\n\r\nF-Statistic = MSGroup\r\n\r\nMSError = Variation BETWEEN groups\r\n\r\nVariation WITHIN groups =\u00a0<\/span>\r\n\r\n<\/div>\r\n
\r\n

Question 4<\/h3>\r\n4) Recall from previous in-class activities that hypothesis testing for two means is\u00a0 based on the t Distribution, and we calculate the test statistic, t. ANOVA is based on\u00a0 the F Distribution, so we will be calculating the F-statistic.\r\n\r\nGo to the DCMP F Distribution tool at https:\/\/dcmathpathways.shinyapps.io\/FDist\/.\r\n\r\nUsing the data analysis tool, graph the F Distribution from the example by entering\u00a0 the degrees of freedom from Question 1, Part C or by selecting varying values.\r\n\r\nPart A: The F Distribution is:\r\n\r\na) Skewed left\r\n\r\nb) Symmetric\r\n\r\nc) Skewed right\r\n\r\nPart B: The t Distribution is symmetric, centered at the mean 0. Thus, when\u00a0 conducting a t-test, we have positive t-values and negative t-values. Adjust\u00a0 the numerator and denominator degrees of freedom in the F Distribution tool.\u00a0 What do you notice about the values in the F Distribution (the values on the\u00a0 horizontal axis)?\r\n\r\na) The F values are always negative.\r\n\r\nb) The F values are always positive.\r\n\r\nc) The F values can be negative or positive.\r\n\r\n<\/div>\r\nAs we just saw, the F-statistic is the ratio of the variation between groups (MSGroup) to the variation within groups (MSError). Larger values of the F-statistic (greater than 1)\u00a0 would imply that the variation between groups is larger than the variation within groups.\r\n
\r\n

Question 5<\/h3>\r\n5) As the variation between groups gets significantly larger than the variation within\u00a0 groups, we will get:\r\n
    \r\n \t
  1. a) A larger F-statistic that corresponds to a greater P-value and less evidence to\u00a0 support the null hypothesis<\/li>\r\n \t
  2. b) A larger F-statistic that corresponds to a smaller P-value and more evidence to\u00a0 support the alternative hypothesis<\/li>\r\n \t
  3. c) A P-value that does not change as the F-statistic changes<\/li>\r\n<\/ol>\r\n<\/div>\r\nWhen there is a greater difference among the group means, the F-statistic will be larger;\u00a0 when there is a smaller difference among the group means, the F-statistic will be\u00a0 smaller.\r\n
    \r\n

    Question 6<\/h3>\r\n6) Which of the following plots will likely have the largest F-statistic? Explain.\u00a0 Note that the means for each group are exactly the same in Plot A and Plot B.\r\n\r\nPlot A\r\n\r\n\"A\r\n\r\nPlot B\r\n\r\n\"A\r\n\r\n<\/div>\r\nRemember that in hypothesis testing, the P-value is our statistical evidence to support\u00a0 our conclusions. When the P-value is less than our significance level, \u03b1, we reject the\u00a0 null hypothesis and have sufficient evidence to support the alternative hypothesis.\u00a0 Otherwise, we fail to reject the null hypothesis and do not have sufficient evidence to\u00a0 support the alternative hypothesis.\r\n
    \r\n

    Question 7<\/h3>\r\n7) Suppose we ran an ANOVA at the alpha (\u03b1) = 0.05 significance level to answer the following question: \u201cIs there a difference in the mean hours of exercise per week\u00a0 among people in the U.S. regions of the Northeast, South, West, and Midwest?\u201d\r\n\r\nPart A: If the test resulted in a P-value of 0.0245, what should you do? a) Reject the null hypothesis.\r\n
      \r\n \t
    1. b) Fail to reject the null hypothesis.<\/li>\r\n \t
    2. c) Accept the null hypothesis.<\/li>\r\n<\/ol>\r\nPart B: Based on your answer to Part A, what would be your conclusion?\r\n
        \r\n \t
      1. a) There is convincing evidence to suggest that there is a difference in the\u00a0 mean hours of exercise between at least two regions.<\/li>\r\n \t
      2. b) There is convincing evidence to suggest that there is a difference in the\u00a0 mean hours of exercise between all four regions.<\/li>\r\n \t
      3. c) There is not convincing evidence to suggest that there is a difference in the mean hours of exercise between the four regions.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
        \r\n

        Question 8<\/h3>\r\n8) Suppose we ran an ANOVA at the alpha (\u03b1) = 0.05 significance level for the\u00a0 following question: \u201cIs there is a difference in the mean reduction of blood pressure\u00a0 for the following three different techniques: diet, exercise, and medication.\u201d\r\n\r\nPart A: If the test resulted in a P-value of 0.3214, what should you do? a) Reject the null hypothesis.\r\n
          \r\n \t
        1. b) Fail to reject the null hypothesis.<\/li>\r\n \t
        2. c) Accept the null hypothesis.<\/li>\r\n<\/ol>\r\nPart B: Based on your answer to Part A, what would be your conclusion?\r\n
            \r\n \t
          1. a) There is convincing evidence that there is a difference in the mean blood\u00a0 pressure reduction between at least two techniques.<\/li>\r\n \t
          2. b) There is convincing evidence that there is a difference in the mean blood\u00a0 pressure reduction between all three techniques.<\/li>\r\n \t
          3. c) There is not convincing evidence that there is a difference in the mean\u00a0 blood pressure reduction between the three techniques.<\/li>\r\n<\/ol>\r\n<\/div>","rendered":"

            Preparing for the next class<\/p>\n

            In the next in-class activity, you will need to make connections between values\u00a0 presented in an ANOVA table and describe the shape of the F Distribution. You will also\u00a0 need to understand how the P-value is represented by an area under an F Distribution\u00a0 curve and describe how the F-statistic is used in hypothesis testing for a one-way\u00a0 ANOVA. Finally, you will need to use the P-value to reach a conclusion.<\/p>\n

            Suppose a researcher wants to investigate the effect of the amount of fertilizer on the\u00a0 height of a common houseplant. More specifically, the researcher is interested in\u00a0 determining if there is a difference in the mean height of plants between those receiving\u00a0 one of following three different fertilizer levels: high, medium, and low.<\/p>\n

            The following data are the simulated results of this controlled experiment. (Note that this\u00a0 small dataset is used introduce the concept and make calculations easier. When\u00a0 conducting an ANOVA, larger sample sizes are usually needed to meet assumptions.)<\/p>\n

            \n\n\n\n\n\n\n
            Fertilizer Level<\/td>\nHeight of Plant (inches)<\/td>\n<\/tr>\n
            Low<\/td>\n23.2, 20.9, 21.5, 25.3<\/td>\n<\/tr>\n
            Medium<\/td>\n24.6, 27.7, 22.5, 30.1<\/td>\n<\/tr>\n
            High<\/td>\n29.2, 30.2, 31.1, 33.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

            As we saw in the previous in-class activity, conducting a one-way ANOVA involves\u00a0 comparing the variation within each of the groups to the variation between each of the\u00a0 groups. When the variation between each of the groups is significantly larger than the\u00a0 variation within each of the groups, we might conclude that there is a statistically significant difference among the means.<\/p>\n

            In an ANOVA table, the calculation illustrating the total variation within the groups of\u00a0 interest is known as the error sum of squares (SSError). The calculation illustrating\u00a0 the total variation between the groups is known as the group sum of squares (SSGroup).<\/p>\n

            Two other essential columns found in an ANOVA table are the degrees of freedom (df) and the mean square.<\/p>\n

            The following table illustrates how these values are calculated for each of the given\u00a0 sources: Group or Error (i.e., between and within).<\/p>\n

            When calculating these values, it is important to know that [latex]k[\/latex] represents the number of\u00a0 groups being considered and [latex]N[\/latex] represents the total number of data values among all\u00a0 groups.<\/p>\n

            \n\n\n\n\n\n\n
            Source<\/td>\nDegrees of Freedom (df)<\/td>\nSum of\u00a0\u00a0Squares<\/td>\nMean\u00a0\u00a0Square<\/td>\nF-Statistic<\/td>\n<\/tr>\n
            Group<\/td>\n[latex]k-1[\/latex]<\/p>\n

            (The number of groups\u00a0 minus 1)<\/td>\n

            		SSGroup<\/td>\nSSGroup<\/p>\n

            [latex]k-1[\/latex]<\/td>\n

            		MSGroup<\/p>\n

            MSError<\/td>\n<\/tr>\n

            Error<\/td>\n[latex]N-k[\/latex]<\/p>\n

            (The total number of data\u00a0 points minus the number of\u00a0 groups)<\/td>\n

            		SSError<\/td>\nSSError<\/p>\n

            [latex]N-k[\/latex]<\/td>\n

            		<\/td>\n<\/tr>\n
            Total<\/td>\n[latex]N-1[\/latex]<\/p>\n

            (The total number of data\u00a0 points minus 1)<\/td>\n

            		SSGroup +\u00a0 SSError<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
            \n

            Question 1<\/h3>\n
            1) Given the information in the previous table, let\u2019s calculate the degrees of freedom\u00a0 associated with the Group and Error sources for the fertilizer and plant height\u00a0 scenario.<\/div>\n

            Part A: In the fertilizer and plant height scenario, what is the value for \ufffd (i.e., the\u00a0 number of groups)?<\/p>\n

            Part B: In the fertilizer and plant height scenario, what is the value for \ufffd (i.e., the\u00a0 total number of data values in the experiment)?<\/p>\n

            Part C: Given your previous responses, complete the Degrees of Freedom column\u00a0 for the fertilizer and plant height scenario in the following table.<\/p>\n

            \n\n\n\n\n\n\n
            Source<\/td>\nDegrees of<\/p>\n

            Freedom (df)<\/td>\n<\/tr>\n

            Group<\/td>\nk \u2212 1 =<\/td>\n<\/tr>\n
            Error<\/td>\nN \u2212 k =<\/td>\n<\/tr>\n
            Total<\/td>\nN \u2212 1 =<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

            When performing a formal hypothesis test for a one-way ANOVA, the mean square\u00a0 values are used to calculate the value of our test statistic; thus, they impact the P-value\u00a0 we get.\u00a0\u00a0<\/span><\/p>\n<\/div>\n

            As noted in the previous table, the mean square for error and mean square for group are calculated by taking each of the sum of square values and dividing them by the\u00a0 degrees of freedom associated with the respective source (i.e., Group or Error).<\/p>\n

            [latex]Mean\\;Square\\;for\\;Error\\;(MSError)=\\frac{Error\\;sum\\;of\\;squares}{degrees\\;of\\;freedom\\;(Error)}=\\frac{SSE}{N-k}[\/latex]<\/p>\n

            [latex]Mean\\;Square\\;for\\;Group\\;(MSGroup)=\\frac{Group\\;sum\\;of\\;squares}{degrees\\;of\\;freedom\\;(Group)}=\\frac{SSG}{k-1}[\/latex]<\/p>\n

            \n

            Question 2<\/h3>\n

            2) We are given the sum of squares and degrees of freedom for the fertilizer and plant\u00a0 height scenario. Use these values to calculate the mean square for error and mean\u00a0 square for group. Enter the values in the following table.<\/p>\n

            \n\n\n\n\n\n\n
            Source<\/td>\nDegrees of<\/p>\n

            Freedom (df)<\/td>\n

            		Sum of Squares<\/td>\nMean Square<\/td>\n<\/tr>\n
            Group<\/td>\n2<\/td>\n55.9134<\/td>\n<\/td>\n<\/tr>\n
            Error<\/td>\n9<\/td>\n140.0108<\/td>\n<\/td>\n<\/tr>\n
            Total<\/td>\n11<\/td>\n195.9242<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
            \n

            Question 3<\/h3>\n

            3) The test statistic that we use to complete the appropriate hypothesis test for a one way ANOVA is calculated with the ratio below:<\/p>\n

            F-Statistic = MSGroup<\/p>\n

            MSError = Variation BETWEEN groups<\/p>\n

            Variation WITHIN groups<\/p>\n

            Use the MSGroup and MSError values you calculated to find the F-statistic for this\u00a0 situation:<\/p>\n

            F-Statistic = MSGroup<\/p>\n

            MSError = Variation BETWEEN groups<\/p>\n

            Variation WITHIN groups =\u00a0<\/span><\/p>\n<\/div>\n

            \n

            Question 4<\/h3>\n

            4) Recall from previous in-class activities that hypothesis testing for two means is\u00a0 based on the t Distribution, and we calculate the test statistic, t. ANOVA is based on\u00a0 the F Distribution, so we will be calculating the F-statistic.<\/p>\n

            Go to the DCMP F Distribution tool at https:\/\/dcmathpathways.shinyapps.io\/FDist\/.<\/p>\n

            Using the data analysis tool, graph the F Distribution from the example by entering\u00a0 the degrees of freedom from Question 1, Part C or by selecting varying values.<\/p>\n

            Part A: The F Distribution is:<\/p>\n

            a) Skewed left<\/p>\n

            b) Symmetric<\/p>\n

            c) Skewed right<\/p>\n

            Part B: The t Distribution is symmetric, centered at the mean 0. Thus, when\u00a0 conducting a t-test, we have positive t-values and negative t-values. Adjust\u00a0 the numerator and denominator degrees of freedom in the F Distribution tool.\u00a0 What do you notice about the values in the F Distribution (the values on the\u00a0 horizontal axis)?<\/p>\n

            a) The F values are always negative.<\/p>\n

            b) The F values are always positive.<\/p>\n

            c) The F values can be negative or positive.<\/p>\n<\/div>\n

            As we just saw, the F-statistic is the ratio of the variation between groups (MSGroup) to the variation within groups (MSError). Larger values of the F-statistic (greater than 1)\u00a0 would imply that the variation between groups is larger than the variation within groups.<\/p>\n

            \n

            Question 5<\/h3>\n

            5) As the variation between groups gets significantly larger than the variation within\u00a0 groups, we will get:<\/p>\n

              \n
            1. a) A larger F-statistic that corresponds to a greater P-value and less evidence to\u00a0 support the null hypothesis<\/li>\n
            2. b) A larger F-statistic that corresponds to a smaller P-value and more evidence to\u00a0 support the alternative hypothesis<\/li>\n
            3. c) A P-value that does not change as the F-statistic changes<\/li>\n<\/ol>\n<\/div>\n

              When there is a greater difference among the group means, the F-statistic will be larger;\u00a0 when there is a smaller difference among the group means, the F-statistic will be\u00a0 smaller.<\/p>\n

              \n

              Question 6<\/h3>\n

              6) Which of the following plots will likely have the largest F-statistic? Explain.\u00a0 Note that the means for each group are exactly the same in Plot A and Plot B.<\/p>\n

              Plot A<\/p>\n

              \"A<\/p>\n

              Plot B<\/p>\n

              \"A<\/p>\n<\/div>\n

              Remember that in hypothesis testing, the P-value is our statistical evidence to support\u00a0 our conclusions. When the P-value is less than our significance level, \u03b1, we reject the\u00a0 null hypothesis and have sufficient evidence to support the alternative hypothesis.\u00a0 Otherwise, we fail to reject the null hypothesis and do not have sufficient evidence to\u00a0 support the alternative hypothesis.<\/p>\n

              \n

              Question 7<\/h3>\n

              7) Suppose we ran an ANOVA at the alpha (\u03b1) = 0.05 significance level to answer the following question: \u201cIs there a difference in the mean hours of exercise per week\u00a0 among people in the U.S. regions of the Northeast, South, West, and Midwest?\u201d<\/p>\n

              Part A: If the test resulted in a P-value of 0.0245, what should you do? a) Reject the null hypothesis.<\/p>\n

                \n
              1. b) Fail to reject the null hypothesis.<\/li>\n
              2. c) Accept the null hypothesis.<\/li>\n<\/ol>\n

                Part B: Based on your answer to Part A, what would be your conclusion?<\/p>\n

                  \n
                1. a) There is convincing evidence to suggest that there is a difference in the\u00a0 mean hours of exercise between at least two regions.<\/li>\n
                2. b) There is convincing evidence to suggest that there is a difference in the\u00a0 mean hours of exercise between all four regions.<\/li>\n
                3. c) There is not convincing evidence to suggest that there is a difference in the mean hours of exercise between the four regions.<\/li>\n<\/ol>\n<\/div>\n
                  \n

                  Question 8<\/h3>\n

                  8) Suppose we ran an ANOVA at the alpha (\u03b1) = 0.05 significance level for the\u00a0 following question: \u201cIs there is a difference in the mean reduction of blood pressure\u00a0 for the following three different techniques: diet, exercise, and medication.\u201d<\/p>\n

                  Part A: If the test resulted in a P-value of 0.3214, what should you do? a) Reject the null hypothesis.<\/p>\n

                    \n
                  1. b) Fail to reject the null hypothesis.<\/li>\n
                  2. c) Accept the null hypothesis.<\/li>\n<\/ol>\n

                    Part B: Based on your answer to Part A, what would be your conclusion?<\/p>\n

                      \n
                    1. a) There is convincing evidence that there is a difference in the mean blood\u00a0 pressure reduction between at least two techniques.<\/li>\n
                    2. b) There is convincing evidence that there is a difference in the mean blood\u00a0 pressure reduction between all three techniques.<\/li>\n
                    3. c) There is not convincing evidence that there is a difference in the mean\u00a0 blood pressure reduction between the three techniques.<\/li>\n<\/ol>\n<\/div>\n","protected":false},"author":23592,"menu_order":6,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5460","chapter","type-chapter","status-publish","hentry"],"part":5448,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5460","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5460\/revisions"}],"predecessor-version":[{"id":5685,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5460\/revisions\/5685"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5448"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5460\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5460"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5460"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5460"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5460"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}