Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.05 level that the medicine relieves pain in less than 335 seconds. For a sample of 50 patients, the mean time in which the medicine relieved pain was 332 seconds. Assume the population standard deviation is 19 .

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6:Find the value of the test statistic. Round your answer to two decimal places

Step 3 of 6:Specify if the test is one-tailed or two-tailed.

Step 4 of 6:Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6:Identify the level of significance for the hypothesis test.

Step 6 of 6:Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Given ,

Sample size = n = 50

Sample mean = = 332

Population standard deviation = = 19

Step 1)

Claim : The medicine relieves pain in less than 335 seconds

i.e In Statistics notation , Claim : < 335

So hypothesis is,

( Claim )

Step 2)

Test statistic :

Population standard deviation is known , so we have to perform one sample Z test.

Formula of test statistic ,

z = -1.1164844 -1.12

Test statistic = z = -1.12

Step 3)

If alternative hypothesis contain 'not equal to ( \= )' sign then it is two tailed test.

If alternative hypothesis contain 'less than ( < )' or 'greater than ( > )' sign then it is two tailed test.

Here , Alternative hypothesis is ,  

So it is one tailed test ( Left tailed )

Step 4)

P-value :

P-value for this left tailed test is ,

P-value = P( Z < test statistic ) = P( Z < -1.1164844 ) { Do not round test statistic for accuracy }

Using Excel function , "=NORMSDIST( z )

P( Z < -1.1164844 ) = NORMSDIST(-1.1164844 ) = 0.132107422

P-value = 0.1321

Step 5)

level of significance = = 0.05

Step 6)

Decision about null hypothesis :

Decision rule :

• Reject null hypothesis if P-value less than = 0.05
• Otherwise fail to reject null hypothesis.

It is observed that P-value ( 0.1321 ) is greater than = 0.05

So Fail to reject null hypothesis.

Conclusion : There is not sufficient evidence to conclude that the medicine relieves pain in less than 335 seconds