Statistical Inference 3

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Gnxrefybir

Mathematics

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Use a provided data file to make a statistical inference to answer a hypothetical question. Write a 1–2 page report to summarize your analysis.

Note: The assessments in this course build upon each other, so you are strongly encouraged to complete them in sequence.

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Statistical Inference 3 Use a provided data file to make a statistical inference to answer a hypothetical question. Write a 1–2 page report to summarize your analysis. Note: The assessments in this course build upon each other, so you are strongly encouraged to complete them in sequence. Use the Mall Time Interview Results file, linked in the Resources under the Required Resources heading, to complete the calculations for this scenario. Practical Application Scenario As the food court manager at the Mall of Elbonia, you want to determine how much time customers spend at the mall at different times of the week (for example: midweek, day; midweek, evening; weekend, day; weekend, evening). Last week, the mall survey staff administered a random survey to mall visitors by selecting customers as they were leaving the mall. One of the questions asked was how much time the customer had spent in the mall on that day. The findings from this study are provided in the Mall Time Interview Results file. In this file, Columns A through D show the time spent by the customers interviewed, according to the weekday and time of day when the interviews occurred. Is there any statistically significant difference (at alpha = .05) in the average amount of time people spent in the mall, based on the weekday and time? To determine the answer to that question, you need to complete the following: • Identify the null and alternative hypotheses you should form for this test. State each as a written explanation and as a math equation. • Identify the appropriate statistical test you should use to accept or reject the null hypothesis. • Calculate the appropriate ANOVA values to accept or reject your null and alternative hypotheses. What should you tell the operators of the Mall of Elbonia's food court stores (in terms of the mall's high-traffic times and customer tendencies)? Summarize your statistical analysis in a report for management. Additional Requirements Compile your work and report in a 1–2 page Microsoft Word file: • Paste in the tables you used to make your calculations. • Clearly title your tables, including each row and column. • Highlight the results of your data calculations within each table. Statistical Inference 3 Scoring Guide Criteria Determine the null hypothesis and alternative hypothesis for making decisions regarding customer tendencies. Proficient Determines the null hypothesis and alternative hypothesis for making decisions regarding customer tendencies. Distinguished Determines an accurate and appropriate null hypothesis and alternative hypothesis for making decisions regarding customer tendencies. Explains the hypothesis statements and accurately expresses the mathematical equation of the hypotheses for testing. Compute the ANOVA values to indicate acceptance or rejection of a null hypothesis regarding customer tendencies. Computes and interprets ANOVA values to indicate acceptance or Computes ANOVA values to rejection of a null indicate acceptance or rejection of hypothesis regarding a null hypothesis regarding customer tendencies, customer tendencies. reports the findings to management, and justifies the interpretation. Compute the appropriate statistical test to determine acceptance or rejection of a null hypothesis. Computes and interprets the appropriate statistical test to determine acceptance or rejection of a null hypothesis, and justifies the interpretation. Computes the appropriate statistical test to determine acceptance or rejection of a null hypothesis. Creates a management report Create a management report Creates a management report summarizing summarizing statistical analysis summarizing statistical analysis on statistical analysis on on customer shopping tendencies. customer shopping tendencies. customer shopping tendencies; provides recommendations for Criteria Proficient Distinguished business opportunities based on findings. Communicates in a manner that is professional, scholarly, and Communicate in a manner that is Communicates in a manner that is consistent with professional and consistent with professional and consistent with expectations for expectations for members of the expectations for members of the members of the business professions. business professions. business professions. Adheres to APA guidelines, and work is appropriate for publication. Mall Time Interview Results Midweek, Day 66 78 66 32 35 34 88 149 86 145 146 38 95 80 106 42 95 77 98 71 122 125 85 97 33 End of worksheet Midweek, Evening 64 71 174 53 52 96 135 142 149 59 82 118 132 81 111 68 22 50 125 105 92 115 148 66 74 Weekend, Day 64 121 29 147 162 108 61 77 88 131 127 141 176 161 3 82 128 51 81 54 161 158 45 134 38 Weekend, Evening 185 207 203 84 125 184 129 94 182 65 110 139 108 117 125 65 47 88 84 165 86 164 199 83 36 Hypothesis statements for a two-tailed test with more than two variables: Remember the Hypothesis statement rules: Null Hypothesis (H0) - The status quo, no change, what we are beginning with - The opposite of what the Claim is Alternative Hypothesis (H1) - The statement with an expected change - The Claim we are testing The easiest way to remember the purpose of the Null and Alternative is to think of the N Here is how you would write the hypthesis equations: First set up the variables: u1=midweek day; u2=midweek evening; u3= weekend day; u4=weeken Third write the Null hypothesis statement and equation: Second write the Alternative hypothesis statement and equation: ts for a two-tailed test with more than two variables: Remember the Hypothesis statement rules: Null Hypothesis (H0) - The status quo, no change, what we are beginning with - The opposite of what the Claim is Alternative Hypothesis (H1) - The statement with an expected change - The Claim we are testing The easiest way to remember the purpose of the Null and Alternative is to think of the Null as the statement with NO Change. Here is how you would write the hypthesis equations: First set up the variables: u1=midweek day; u2=midweek evening; u3= weekend day; u4=weekend evening Third write the Null hypothesis statement and equation: Null Hypothesis: There is not a significant difference in the amount of time customers spend in the mall based on day and time H0: u1 = u2 = u3 = u4 H0: where there is no significant difference between the variables Second write the Alternative hypothesis statement and equation: Alternative Hypothesis: The claim is there is a significant difference in the amount of time customers spend in the mall based on day and time H1: u1 ≠ u2 ≠ u3 ≠ u4 H1: where any one variable is not equal to another Run the ANOVA single factor that is in the Data Analysis Toolkit provided in Excel. ANOVA's are great since you notice there is only one variable input range. So, you highlight the ENTIRE table. Table data range goes here. Ensure box is checked Alpha is set Opens in new worksheet Results will open in a new worksheet Finally click on OK Anova: Single Factor SUMMARY Groups Midweek, Day Midweek, Evening Weekend, Day Weekend, Evening Count 25 25 25 25 ANOVA Source of Variation Between Groups Within Groups SS 20487.119 187749.370 Total 208236.489 Sum 2087.899 2384.000 2528.000 3074.000 df 3 96 Average 83.516 95.360 101.120 122.960 MS 6829.040 1955.723 Variance 1300.167 1479.657 2434.610 2608.457 F 3.492 P-value 0.019 F crit 2.699 99 P-value of 0.019 is less than our alpha of which means we accept the alternative h The amount time people spend in the ma People spend the most time at the mall d Weekend days. This means management the weekend evenings. Need more staff during weekend evening me people spend in the mall is statistically significant based on day and time. Anova: Single Factor SUMMARY Groups Midweek, Day Midweek, Evening Weekend, Day Weekend, Evening Count 25 25 25 25 ANOVA Source of Variation Between Groups Within Groups SS 20487.12 187749.37 Total 208236.49 Sum 2087.90 2384.00 2528.00 3074.00 df 3 96 Average 83.52 95.36 101.12 122.96 MS 6829.04 1955.72 Variance 1300.17 1479.66 2434.61 2608.46 F 3.492 P-value 0.019 F crit 2.699 99 You will want to Google: F Test Statistic, to pro If the Test Statistic F is greater than the F critical value we will reject the NULL to Google: F Test Statistic, to provide justification as to when and why you would use the F-Test vs the P-value. Then provide an intext citation and add source to the reference section. Mall Time Interview Results Midweek, Day 66 78 66 32 35 34 88 149 86 145 146 38 95 80 106 42 95 77 98 71 122 125 85 97 33 End of worksheet Midweek, Evening 64 71 174 53 52 96 135 142 149 59 82 118 132 81 111 68 22 50 125 105 92 115 148 66 74 Weekend, Day 64 121 29 147 162 108 61 77 88 131 127 141 176 161 3 82 128 51 81 54 161 158 45 134 38 Weekend, Evening 185 207 203 84 125 184 129 94 182 65 110 139 108 117 125 65 47 88 84 165 86 164 199 83 36
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Running head: STATISTICAL INFERENCE 3

Statistical Inference 3
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