**Title: Evaluating the Impact of Laboratory Techniques Education on Student Safety****Introduction:**Mandrake Falls High School faces significant financial losses due to accidents and equipment misuse in its laboratories. In response, a weekend course on laboratory techniques was introduced, targeting enhancing student safety and reducing incidents.**Objective:**To assess whether taking the laboratory techniques course influences students' laboratory performance and incident involvement.**Data Structure:**The analysis involves a contingency table that categorizes students based on their laboratory performance, split into three groups: 1. Involved in no incident2. Involved in exactly one incident3. Involved in two or more incidentsAdditionally, students are divided into those who took and did not take the techniques course.**Contingency Table Format:**| Status regarding lab techniques course | Involved in no incident | Involved in exactly one incident | Involved in 2+ incidents | Total ||----------------------------------------|------------------------|---------------------------------|--------------------------|-------|| Took the techniques course | 35 | 28 | 12 | 75 || Didn’t take the techniques course | 69 | 33 | 23 | 125 || Total | 104 | 61 | 35 | 200 |*Note: Includes expected frequencies (e.g., 13.13, 0.097) and chi-square calculations within each cell.***Part 1: Table Completion**Your task is to fill in the missing values using the provided formula:\[\frac{( \text{Observed cell frequency} - \text{Expected cell frequency})^2}{\text{Expected cell frequency}}\]**Part 2: Statistical Analysis**To determine the hypothesis:- **Null Hypothesis (H₀):** No relationship exists between students' laboratory performances and whether they took the techniques course.- **Tasks:** (a) Determine type of test statistic (e.g., Chi-square). (b) Calculate the test statistic value, rounding to two decimal places. (c) Find the critical value for a 0.10 significance level, rounded to two decimal places. (d) Decide if there is a relationship by using the 0.10 level of significance. **Conclusion:**This study aims to provide insights into whether educational interventions, like the laboratory techniques course, effectively enhance students

a) It is needed to test, whether there is a relationship between students’ laboratory performance…

Mandrake Falls High School is losing a lat of money through its school laboratories. Accidents and misuse of equipment by students are taking their toll on laboratory supplies. In an attempt to remedy this, Mandrake is experimenting with a weekend cnurse in laboratory techniques. For the time being, lack of resources allow anly a portion of Mandrake's lab students to take the weekend course: of the 200 students enrolled in lab classes at Mandrake, only 75 have been able to take the weekend course. Mandrake is interested in evaluating the course's effectiveness in propagating safety in the laboratories. During regular lab classes, lab instructors are recording harmful lab incidents: accidents, misuse of lab equipment, etc. The high school is looking at the data and examining two variables: laboratory performance ("invalved in no incident", "Invalved in exactly one indident", or "Involved in 2+ Incidents") and status regarding lab techniques course ("tock the techniques course" or "didn't take the techniques course"). The cantingnney tahle below gives a summary of the data that have been gathered so far. In each of the 6 cnils of the table are three numbers: the first number is the observed cell frequency fo): the second number is the pxpected cell frequency e) under the assumption that there is no relationship between students' laboratory performances and whether or not they took the techniques course; and the third number is the following valua. (fo-fe) (obsarved cell frequency"Expected cell frequency) Expected cell frequency The numbers labeled "Total" are totals for observed frequency. Part 1 Fil in the missing values in the contingency table. Round your expected frequencies to two or more decimal places, and round your values to three ar more decimal places. Sond data to Excel Laboratory performance Involved in Involved in Involved in ехactiy one Total no incident 2+ incidents incident 35 28 12 Took the techniques 13.13 75 course Status regarding 0.097 lab 69 33 23 Didn't take techniques the 21.88 125 course techniques course 0.057 Total 104 61 35 200 Part 2 Answer the following to summarize the test of the hypothesis that there is no relationship between students' laboratory performances and whether or not they took the techniques course. For your test, use the 0.10 Invel of significance- (a) Determine the type of test statistic to use. Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round to two or more decimal places.) (e) Find the critical valun for a test at the 0.10 level of significance. (Round to two or mare decimal places.) (d) Can Mandrake condlude that there is a relationship between students' laboratory performances and whether or not they took the techniques course? Use the 0.10 level of significance. O Yes O No