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Solve this question only for parts D, E and F.

Solve this question only for parts D, E and F.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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Solve this question only for parts D, E and F.

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. =
e. State the rejection region (in the form of inequality). The rejection region is f. Decide whether null hypothesis is rejected or is not rejected, and insert the word rejected or the words not rejected into the following statement. Null hypothesis is_ Insert the word sufficient or insufficient into the following statement. There is _sample evidence to conclude that there is a difference in mean recovery time after surgical procedure I and mean recovery time after surgical procedure II.
Transcribed Image Text:e. State the rejection region (in the form of inequality). The rejection region is f. Decide whether null hypothesis is rejected or is not rejected, and insert the word rejected or the words not rejected into the following statement. Null hypothesis is_ Insert the word sufficient or insufficient into the following statement. There is _sample evidence to conclude that there is a difference in mean recovery time after surgical procedure I and mean recovery time after surgical procedure II.
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