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To compare the mean lengths of time to recovery after two surgical procedures I and II, 10 patients after surgical procedure I were randomly selected, and the length of time to recovery was recorded for each patient. Also 10 patients after surgical procedure II were randomly selected, and the length of time to recovery was recorded for each patient. Calculated values of sample mean and sample variances are given in the following table:

To compare the mean lengths of time to recovery after two surgical procedures I and II, 10 patients after surgical procedure I were randomly selected, and the length of time to recovery was recorded for each patient. Also 10 patients after surgical procedure II were randomly selected, and the length of time to recovery was recorded for each patient. Calculated values of sample mean and sample variances are given in the following table:

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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To compare the mean lengths of time to recovery after two surgical procedures I and II, 10 patients after surgical procedure I were randomly selected, and the length of time to recovery was recorded for each patient. Also 10 patients after surgical procedure II were randomly selected, and the length of time to recovery was recorded for each patient. Calculated values of sample mean and sample variances are given in the following table: Procedure I x₁ = 7.7 days s² =1.25 days squared Procedure Il x₂ = 9.8 days $²=1 =1.50 days squared For both surgical procedure the length of time to recovery is normal random variable. Do the data provide sufficient sample evidence to indicate a difference in the mean recovery time after surgical procedure I and mean recovery time after surgical procedure II? Test appropriate hypotheses. Use a = 0.05. Assume that population variances may be assumed equal and common population variance is estimated with the value of pooled sample variance. a. State null and research hypotheses about the difference in mean recovery times. H: H₁: b. State the value of pooled sample variance. Keep three digits after decimal point in the answer. Show your work in finding pooled sample variance. The value of pooled sample variance is $² c. State the observed value of test statistic Keep three digits after decimal point in the answer. d. Show your work in finding the observed value of test statistic. The observed value of test statistic is t obs. =
Transcribed Image Text:To compare the mean lengths of time to recovery after two surgical procedures I and II, 10 patients after surgical procedure I were randomly selected, and the length of time to recovery was recorded for each patient. Also 10 patients after surgical procedure II were randomly selected, and the length of time to recovery was recorded for each patient. Calculated values of sample mean and sample variances are given in the following table: Procedure I x₁ = 7.7 days s² =1.25 days squared Procedure Il x₂ = 9.8 days $²=1 =1.50 days squared For both surgical procedure the length of time to recovery is normal random variable. Do the data provide sufficient sample evidence to indicate a difference in the mean recovery time after surgical procedure I and mean recovery time after surgical procedure II? Test appropriate hypotheses. Use a = 0.05. Assume that population variances may be assumed equal and common population variance is estimated with the value of pooled sample variance. a. State null and research hypotheses about the difference in mean recovery times. H: H₁: b. State the value of pooled sample variance. Keep three digits after decimal point in the answer. Show your work in finding pooled sample variance. The value of pooled sample variance is $² c. State the observed value of test statistic Keep three digits after decimal point in the answer. d. Show your work in finding the observed value of test statistic. The observed value of test statistic is t obs. =
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