Using the following table:1. Determine a hypothesis to test the relationship between months enrolled and height of students, identify the appropriate type of statistical test to test the hypothesis and perform the statistical test (please show steps)IDSchool EnrolledMonths enrolledBirthday monthDistance to WorkHeightFoot SizeHand SizeSleepHomework1Arts and Sciences12January06085360302Applied Science and Technology6February06276400453Business and Management8April566107420604Nursing10June1068128440155Public Service48July1568148540756Arts and Sciences48June30701294801207Applied Science and Technology36October3272128320808Applied Science and Technology32November3675147440609Nursing6July863973009010Arts and Sciences22May22801494203011Business and Management15February1065865006012Public Service20April4711084002013Applied Science and Technology11March1566974406014Arts and Sciences18November2864973003015Arts and Sciences29January12721083608016Nursing13December6638648010017Business and Management49August0791394102518Applied Science and Technology16April10741284301519Business and Management24September30661063306020Arts and Sciences8May0659748030

Name: Using the following table:1. Determine a hypothesis to test the relat
Uploaded: 2024-03-20T07:07:12.000Z
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Description: Using the following table:1. Determine a hypothesis to test the relationship between months enrolled and height of students, identify the appropriate type of statistical test to test the hypothesis and perform the statistical test (please show steps

Appropriate test: The investigator is specially interested to test whether there isa ny significant relationship between the variables month enrolled and height. In order to test the hypothesis regarding the direction of relation between a paired set of n observations (xi, yi), a significance test for correlation is appropriate. Hence, the appropriate statistics is correlation. Thus, the sampling distribution used in the given scenario is “Student’s t”. Denote r as the sample correlation coefficient between months enrolled and height and ρ as the population correlation coefficient between months enrolled and height. The null and alternate hypotheses are stated below: Null hypothesis H0: H0: ρ = 0 That is, there exist no significant relationship between the variable’s months enrolled and height. H1: ρ ≠ 0 That is, there exist a significant relationship between the variable’s months enrolled and height. To find the relationship between the variable’s months enrolled and height, correlation coefficient should be calculated. Correlation can be calculated using EXCEL software: Software Procedure: The step-by-step procedure to obtain correlation coefficient using EXCEL software is given below: Open an EXCEL file. Enter the data of values of the variable months enrolled in column A and name it as Months enrolled. Enter the data of values of the variable Height in column B and name it as Height. In any cell, enter the formula "CORREL(A2:A21,B2:B21)”. Click OK. The generated output is given below: Thus, the correlation coefficient between the variables months enrolled and height is r = 0.5904.Test statistic: The sample test statistic is obtained as 3.1036 from the calculations given below: Therefore, the test statistic value is 3.1036. Critical value: Since, the level of significance is not specified, the prior level of significance α = 0.05 can be used. The critical value is obtained as ±2.1009 from the calculation given below: Since, the t-distribution is symmetric, the two critical values are –t(α/2) = -2.1009 and +t(α/2) = +2.1009. Decision rule: Denote t as test statistic value and t(α/2) as the critical value. Decision rule based on critical approach: If t ≤ –t(α/2) (or) t ≥ t(α/2), then reject the null hypothesis H0. If –t(α/2) < t < t(α/2), then fail to reject the null hypothesis H0. Conclusion: Conclusion based on critical value approach: The test statistic value is 3.1036 and critical value is ±2.1009 Here, t > t(α/2). That is, 3.1036 (=t) > 2.1009 (= t(α/2)). By the rejection rule, reject the null hypothesis H0. Thus, there exist a significant relationship between the variable’s months enrolled and height. Since, the correlation is positive, there exist a positive relationship between the variable’s months enrolled and height.