Use the information given below to answer the next six questions The director of

Question

Use the information given below to answer the next six questions The director of research and development is testing a new medicine, E-XPAIN. She wants to less than 6.5 minutes know if there is evidence at the 0.0i level that the medicine relieves pain in (390 seconds). For a sample of 41 patients, the mean time in which the medcine was 382 seconds. Assume the population standard deviation is known to be 21 secon What are the null hypothesis and alternative hypothesis for this test? A. Ho: -39011a: 390 C. Ho: 390 Ha: 390 E. Ho: H390 Ha: > 390 382 382 . B. Ho: -382 D. Ilo: -382 Ha: Ha. 2. What test statistic is most appropriate? aZ b.t c. chi-square Assume that you should be using a z-table. What is the absolute critical (table) value of the test statistic? A. 1.645 E. 2.57 B. 1.96 C. 2.33 D. -2.44 4. What is the test statistic (i.e. calculated) value? A. 0 B. -2.44 C. -2.33 D. +2.44 E. +2.33 Assuming the calculated value of the test statistic is -2.36, what are the decision and conclusion of the test? A. Fail to reject the null hypothesis, conclude there is overwhelming evidence that the medicine relieves pain in less than 390 seconds B. Reject the null hypothesis, conclude there is evidence that the medicine relieves pain in less than 390 seconds. C. Fail to reject the null hypothesis, conclude there is insufficient evidence that the medicine relieves pain in less than 390 seconds. D. Fail to reject the null hypothesis, conclude there is evidence that the medicine relieves pain in less than 390 seconds. E. Reject the null hypothesis, conclude there is insufficient evidence that the medicine relieves pain in less than 390 seconds. sume that the p-value is found to be 0.004. What are the decision and conclusion of the .Fail to reject the null hypothesis, conclude there is overwhelming evidence that the medicine relieves pain in less than 390 seconds Reject the null hypothesis, conclude there is evidence that the medicine relieves pain in less than 390 seconds. Fail to reject the null hypothesis, conclude there is insufficient evidence that the medicir relieves pain in less than 390 seconds. Fail to reject the null hypothesis, conclude there is evidence that the medicine relieves pain in less than 390 seconds. Reject the null hypothesis, conclude there is insufficient evidence that the medicine elieves pain in less than 390 seconds.

Explanation / Answer

Given that,
population mean(u)=390
standard deviation, sigma =21
sample mean, x =382
number (n)=41
null, Ho: >=390
alternate, H1: <390
level of significance, alpha = 0.01
from standard normal table,left tailed z alpha/2 =2.326
since our test is left-tailed
reject Ho, if zo < -2.326
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 382-390/(21/sqrt(41)
zo = -2.44
| zo | = 2.44
critical value
the value of |z alpha| at los 1% is 2.326
we got |zo| =2.44 & | z alpha | = 2.326
make decision
hence value of | zo | > | z alpha| and here we reject Ho
p-value : left tail - ha : ( p < -2.44 ) = 0.01
hence value of p0.01 < 0.01, here we do not reject Ho

ANSWERS
---------------
null, Ho: >=390 ,alternate, H1: <390, Z test
critical value: 2.33
test statistic: -2.44
decision: reject Ho
p-value: 0.01

have enough evidence that medicine relives pain in less than 6.5 min

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.