# MATHEMATICS

The following 13 questions (Q1 to Q13) are based on the following example:

Patients recovering from an appendix operation normally spend an average of 6.3 days in the hospital. The distribution of recovery times is normal with a σ = 2.0 days. The hospital is trying a new recovery program designed to lessen the time patients spend in the hospital. The first 16 appendix patients in this new program were released from the hospital in an average of 5.8 days. On the basis of these data, can the hospital conclude that the new program has a significant reduction of recovery time. Test at the .05 level of significance.

Q1: The appropriate statistical procedure for this example would be a

A. t-test

B. z-test

Q2: Is this a one-tailed or a two-tailed test?

A. one-tailed

B. two-tailed

Q3: The most appropriate null hypothesis (in words) would be

A. There is no statistical difference in the amount of time appendix patients

spend in the hospital when comparing the new recovery program to the

population of patients on the traditional recovery program.

B. There is a statistical difference in the amount of time appendix patients spend

in the hospital when comparing the new recovery program to the population of

patients on the traditional recovery program.

C. The new appendix recovery program does not significantly reduce the number

of days spent in the hospital when compared to the population of patients on

D. The new appendix recovery program does significantly reduce the number of

days spent in the hospital when compared to the population of patients on the

Q4: The most appropriate null hypothesis (in symbols) would be

A. μnew program = 6.3

B. μnew program = 5.8

C. μnew program ≤ 6.3

D. μnew program ≥ 6.3

Q5: 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:

Q6: What is the numeric value of your standard error?

Q7: What is the z-value or t-value you obtained (your test statistic)?

A. reject the null hypothesis

B. fail to reject the null hypothesis

Q9: The best conclusion for this example would be

A. There is no statistical difference in the amount of time appendix patients

spend in the hospital when comparing the new recovery program to the

population of patients on the traditional recovery program.

B. There is a statistical difference in the amount of time appendix patients spend

in the hospital when comparing the new recovery program to the population of

patients on the traditional recovery program.

C. The new appendix recovery program does not significantly reduce the number

of days spent in the hospital when compared to the population of patients on

D. The new appendix recovery program does significantly reduce the number of

days spent in the hospital when compared to the population of patients on the

Q10: Based on your evaluation of the null in Q8 and your conclusion is Q9, as a researcher you would be more concerned with a

A. Type I statistical error

B. Type II statistical error

Calculate the 95% confidence interval.

Steps:

Q11: The mean you will use for this calculation is

A. 5.8

B. 6.3

Q12: What is the new critical value you will use for this calculation?

Q13: As you know, two values will be required to complete the following equation:

The following 4 questions (Q14 to Q17) are based on the following situation:

If α = .04, and β = .35, complete the following questions by inserting the appropriate

probability of each.

Q14: The statistical decision is to reject the null, and H0 is really true (ie: a Type I error)

Q15: The statistical decision is to fail to reject null, and H0 is really true (ie: a correct decision)

Q16: The statistical decision is to reject the null, and H0 is really false (ie: Power)Q17: x

The statistical decision is to fail to reject the null, and H0 is really false

(ie a Type II error)

The following 14 questions (Q18 to Q31) 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 1200 on the SAT, with a sample standard deviation of 100. 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 .01.

Q18: The appropriate statistical procedure for this example would be a

A. t-test

B. z-test

Q19: Is this a one-tailed or a two-tailed test?

A. one-tailed

B. two-tailed

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