Question

The following 14 questions (Q78 to Q91) are based on the following example:

A researcher wants to determine whether high school students who attend an SAT preparation course score significantly different on the SAT than students who do not attend the preparation course. For those who do not attend the course, the population mean is 1050 (μ = 1050). The 16 students who attend the preparation course average 1150 on the SAT, with a sample standard deviation of 300. On the basis of these data, can the researcher conclude that the preparation course has a significant difference on SAT scores? Set alpha equal to .05.

Q78: The appropriate statistical procedure for this example would be a

• A. z-test
• B. t-test

Q79: Is this a one-tailed or a two-tailed test?

• A. one-tailed
• B. two-tailed

Q80: The most appropriate null hypothesis (in words) would be

• A. There is no statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.
• B. There is a statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.
• C. The students who took the SAT prep course did not score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.
• D. The students who took the SAT prep course did score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.

Q81: The most appropriate null hypothesis (in symbols) would be

• A. μ_SATprep = 1050
• B. μ_SATprep = 1150
• C. μ_SATprep 1050
• D. μ_SATprep 1050

Q82: Set up the criteria for making a decision. That is, find the critical value using an

alpha = .05. (Make sure you are sign specific: + ; - ; or ) (Use your tables)

Summarize the data into the appropriate test statistic.

Steps:

Q83: What is the numeric value of your standard error?

Q84: What is the z-value or t-value you obtained (your test statistic)?

Q85: Based on your results (and comparing your Q84 and Q82 answers) would you

• A. reject the null hypothesis
• B. fail to reject the null hypothesis

Q86: The best conclusion for this example would be

• A. There is no statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.
• B. There is a statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.
• C. The students who took the SAT prep course did not score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.
• D. The students who took the SAT prep course did score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.

Q87: Based on your evaluation of the null in Q85 and your conclusion is Q86, as a researcher you would be more concerned with a

• A. Type I statistical error
• B. Type II statistical error

Calculate the 99% confidence interval.

Steps:

Q88: The mean you will use for this calculation is

• A. 1050
• B. 1150

Q89: What is the new critical value you will use for this calculation?

Q90: As you know, two values will be required to complete the following equation:

__________ __________

Q91: Which of the following is a more accurate interpretation of the confidence interval you just computed?

• A. We are 99% confident that the scores fall in the interval _____ to _____.
• B. We are 99% confident that the average score on the SAT by the students who took the prep course falls in the interval _____ to _____.
• C. We are 99% confident that the example above has correct values.
• D. We are 99% confident that the difference in SAT scores between the students who took the prep course and the students who did not falls in the interval _____ to _____.

Answer 1

78) Option - B) t-test

Since, is unknown and the sample size is less than 30.

79) Option - B) two-tailed

80) Option - A) There is no statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.

81) Option - A)

82) df = 16 - 1 = 15

At alpha = 0.05, the critical values are +/- t_0.025,15 = +/- 2.131

Reject H₀, if t < -2.131 or, t > 2.131

83) SE = s/ = 300/ = 75

84) The test statistic is

  

85) Since the test statistic value lies in the critical region, so we should reject the null hypothesis.

Option - A) Reject the null hypothesis.

86) Option - B) There is a statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.

87) Option - A) Type I statistical error.

88) Option - A) 1150

89) At 99% confidence level, the critical value is t^* = 2.947

90) The 99% confidence interval is

91) Option - B) We are 99% confident that the average score on the SAT by the students who took the prep course falls in the interval 928.975 to 1371.025.