Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 340 seconds. For a sample of 52 patients, the mean time in which the medicine relieved pain was 347 seconds. Assume the population standard deviation is 18. Step 1 of 6 : State the null and alternative hypotheses.

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.020.02 level that the medicine relieves pain in more than 340340 seconds. For a sample of 5252 patients, the mean time in which the medicine relieved pain was 347347 seconds. Assume the population standard deviation is 1818.

Step 1 of 6 :  

State the null and alternative hypotheses.

please solve all steps

Answer 1

given data are:-

sample mean() = 347

sample size (n) = 52

population sd () = 18

hypothesis:-

the claim is the alternative hypothesis.

test to be used:-

here, as the population sd is known, and n > 30...we will do 1 sample Z test for mean.

test statistic is:-

p value is:-

[ in any blank cell of excel type =NORMSDIST(2.8043)]

decision:-

p value = 0.0025 < 0.02 (alpha)

so, we reject the null hypothesis.

conclusion:-

there is sufficient evidence to support the claim that the medicine relieves pain in more than 340 seconds at 0.02 level of significance.

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