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Statistical Evaluation of the Impact of an SAT-Math Tutoring Program on Student Scores

This Statistics Analysis Homework is concerned with the research scenario of a high school counselor who has set out to investigate the effects of an SAT-math tutoring program that spans 8 weeks. To scrutinize this hypothesis, the counselor successfully recruited 17 students to engage in the SAT-math tutoring program for the full duration. The students' scores were meticulously collected and subjected to a statistical program that conducted z-tests. The critical question at hand is whether the SAT-math tutoring students' scores exhibit a significant increase when contrasted with the national norm, and this test is conducted at a significance level (alpha) of 0.05.

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Problem Description:

A high school counselor plans to run an SAT-math tutoring program for 8 weeks. He believes this tutoring program will result in participating students having higher SAT-math scores compared to the norm (μ=500, σ=100). The counselor can get 17 students to participate in the SAT-math tutoring program for the full 8 weeks. The counselor collected scores from the sample of students who participated in the program and compared them to the norm with a statistical program that would run z-tests (see output table below). Are the SAT-math tutoring students’ scores significantly higher when compared to the norm? Test at the .05 alpha level.

Output Table

Variablen Sample Mean Std .Err. Z -Stat P -value
17varl 525.82355 24.253563 1.0647314 0.1435

Solution

Directions: Complete the items based on the scenario and output table above.

  1. Independent Variable = Categorical
  2. Dependent Variable = Continuous
  3. one-tailed
  4. Alternative Hypothesis in sentence form (H1):SAT-math tutoring students’ scores higher when compared to the norm
  5. Null Hypothesis in sentence form (H0): SAT-math tutoring students’ scores similar to the norm
  6. zcalculated = 1.0647314
  7. Level of Significance (p) =0.1435
  8. fail to reject null
  9. Write your conclusion in sentence form with appropriate statistics.

There is not sufficient evidence to support the claim that SAT-math tutoring students’ scores significantly higher when compared to the norm