please show calc functions ti-84 6.A study was performed to examine the personal goals of children in grades 4, 5, and 6. A random sample of studentswas selected from grades 4, 5, and 6 from schools in a certain state. They were asked what they would most like to doat school: make good grades, be popular, or excel in sports. Results follow:a.Personal GoalsMake Good GradesBe PopularExcel in SportsBoys7532154Girls2954540Conduct a test of hypothesis to see if gender and personal goals of students have a relationship, use a significancelevel of .05. Show the 5 steps and use the x² - - test function on your calculator to make a decision. Report theexpected value matrix as well.b. Compute the Phi-coefficient, and interpret it in terms of the variables.

Given information: Personal Goals Boys Girls Total Make Good Grades 75 295 370 Be Popular 32 45 77 Excel in Sports 154 40 194 Total 261 380 641a) Null hypothesis: H0: Gender and personal goals of students are independent. Alternate hypothesis: HA: Gender and personal goals of students are not independent. For this analysis, the significance level is 0.05. Using the sample data, we will conduct a chi-square test for independence. Use the given data to form an excel table consisting of observed frequency, expected probability, expected frequency and chi square statistics. Formula for the expected frequency is: Er,c=nr×ncn Personal Goals Boys Expected (Or,c-Er,c)2Er,c Girls Expected (Or,c-Er,c)2Er,c Total Make Good Grades 75 151 38 295 219 26 370 Be Popular 32 31 0 45 46 0 77 Excel in Sports 154 79 71 40 115 49 194 Total 261 261 109 380 380 75 641Use the table to determine the chi-square statistic, degree of freedom and P-value. D.F=(r-1)×(c-1)=(3-1)×(2-1)=2χ2=∑(Or,c-Er,c)2Er,c =184.253555715379≈184.25 Use the excel formula, "=CHISQ.DIST.RT(184.25,2)" for determining the P-value from the chi-square statistic having degrees of freedom 2. P(χ2>184.25)= 0.000 Since the P-value (0.000) is less than the significance level (0.05), we have to reject the null hypothesis. Thus, we conclude that there is a relationship between Gender and personal goals of students.b) ϕ=χ2N=184.25641=0.287441498=0.536135708≈0.536 The value of Phi-coefficient ϕ is 0.536. Phi Coefficient lies between -1 and 1 where: -1 indicates a perfectly negative relationship between the two variables. 0 indicates no association between the two variables. 1 indicates a perfectly positive relationship between the two variables. In the given scenario, Phi-coefficient ϕ of 0.536 there is moderate relationship between Gender and personal goals of students.Calc functions for ti-84: Step 1) First, input the data into a matrix. Press 2nd and then press x-1. Scroll over to Edit, highlight any matrix that is blank and press ENTER. Choose the number of rows(3) and columns (2) to use in the matrix and enter the raw data. Step 2) Press stat and scroll over to TESTS. Then scroll down to X2-Test and Press ENTER. Step 3) Choose the matrix we entered the data for Observed. For Expected, it can be any empty matrix because calculator automatically evaluates the expected values. Step 4) Highlight Calculate and press ENTER. Output: