Using the latest in medical technology, an orthopedic doctor has developed a new surgical procedure that he believes is an improvement over the standard procedure. He wants to study whether the mean recovery time of patients who have the new procedure is less than the mean recovery time of patients who have the standard procedure. The doctor studies a random sample of 11 patients who have the new procedure and a random sample of 10 patients who have the standard procedure. (These samples are chosen independently.) The doctor records each patient's recovery time (in days). These data are shown in the table. New procedure Standard procedure Send data to calculator Recovery times (in days) 395, 428, 317, 330, 391, 397, 376, 350, 362, 291, 395 400, 351, 410, 383, 393, 395, 386, 369, 381, 411 Send data to Excel Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 level of significance, that the population mean of the recovery times of patients who have the new procedure is less than the population mean of recovery times of patients who have the standard procedure? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternate hypothesis H₁. Ho: O H₁:0 (b) Determine the type of test statistic to use. Chi-square Degrees of freedom: H |x X 7 O S 8 0=0 OSO Р

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Using the latest in medical technology, an orthopedic doctor has developed a new surgical procedure that he believes is an improvement over the standard
procedure. He wants to study whether the mean recovery time of patients who have the new procedure is less than the mean recovery time of patients who
have the standard procedure.
The doctor studies a random sample of 11 patients who have the new procedure and a random sample of 10 patients who have the standard procedure. (These
samples are chosen independently.) The doctor records each patient's recovery time (in days). These data are shown in the table.
New procedure
Standard procedure
Send data to calculator
Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 level of significance, that the
population mean of the recovery times of patients who have the new procedure is less than the population mean of recovery times of patients who have the
standard procedure?
(a) State the null
Recovery times (in days)
395, 428, 317, 330, 391, 397, 376, 350, 362, 291, 395
400, 351, 410, 383, 393, 395, 386, 369, 381, 411
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
Ho and the alternate hypothesis H₁.
Send data to Excel
Chi-square
HO
H₁:0
(b) Determine the type of test statistic to use.
(c) Find thou
Degrees of freedom:
dhe th
μ
|x
5
0=0
O
S
On
Р
<Q
חוח
OSO 020
Es
6
E
Transcribed Image Text:Using the latest in medical technology, an orthopedic doctor has developed a new surgical procedure that he believes is an improvement over the standard procedure. He wants to study whether the mean recovery time of patients who have the new procedure is less than the mean recovery time of patients who have the standard procedure. The doctor studies a random sample of 11 patients who have the new procedure and a random sample of 10 patients who have the standard procedure. (These samples are chosen independently.) The doctor records each patient's recovery time (in days). These data are shown in the table. New procedure Standard procedure Send data to calculator Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 level of significance, that the population mean of the recovery times of patients who have the new procedure is less than the population mean of recovery times of patients who have the standard procedure? (a) State the null Recovery times (in days) 395, 428, 317, 330, 391, 397, 376, 350, 362, 291, 395 400, 351, 410, 383, 393, 395, 386, 369, 381, 411 Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) Ho and the alternate hypothesis H₁. Send data to Excel Chi-square HO H₁:0 (b) Determine the type of test statistic to use. (c) Find thou Degrees of freedom: dhe th μ |x 5 0=0 O S On Р <Q חוח OSO 020 Es 6 E
Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 level of significance, that the
population mean of the recovery times of patients who have the new procedure is less than the population mean of recovery times of patients who have the
standard procedure?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis Ho and the alternate hypothesis H₁.
H₂ : O
H₁ :0
(b) Determine the type of test statistic to use.
Chi-square
Degrees of freedom:
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the critical value. (Round to three or more decimal places.)
(e) At the 0.01 level of significance, can the doctor conclude that the mean
recovery time of patients who have the new procedure is less than the mean
recovery time of patients who have the standard procedure?
Yes No
μ
Ix
X
5
a
50
X
S
2
0=0 OSO
#0 0<0
Р
S
<o
Olo
ロマロ
>O
Transcribed Image Text:Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 level of significance, that the population mean of the recovery times of patients who have the new procedure is less than the population mean of recovery times of patients who have the standard procedure? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternate hypothesis H₁. H₂ : O H₁ :0 (b) Determine the type of test statistic to use. Chi-square Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places.) (e) At the 0.01 level of significance, can the doctor conclude that the mean recovery time of patients who have the new procedure is less than the mean recovery time of patients who have the standard procedure? Yes No μ Ix X 5 a 50 X S 2 0=0 OSO #0 0<0 Р S <o Olo ロマロ >O
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