Question

the director of research and development is testing a new drug. she wants to know if there is evidence at the 0.05 level that the drug stays in the system for more than 397 minutes. for a sample of 35 patients, the mean time the drug stayed in the system was 403 minutes. assume the population standard deviation is 18. find the p-value of the test statistic. round your answer to four decimal places.

Answer 1

By using the concept of mean and standard deviation, it can be inferred that

The the drug stays in the system for more than 397 minutes

What is mean and Standard Deviation?

Suppose there is a data set and the average of the data set has to be calculated. To calculate the average of the data set, mean is used

To know about Standard Deviation, it is important to know about Variance

Variance is the sum of the square of deviation from mean.

Square root of the variance gives the standard deviation

Given n = 35,

$\bar{x} = 403,$

Population mean $\\ (\mu)$ = 397

Population Standard Deviation $\\(\sigma)$ = 18

Here the sample size is large. So the distribution is approximately normal

To test :

$H_ 0 = \mu \leq 397\\H_1 = \mu > 397$

Test statistic t = $\frac{403 - 397}{\frac{18}{\sqrt{35}}}$

                       = 1.97

p value at $\alpha = 0.05$ = 0.0244

Since 0.0244 < 0.05, the null hypothesis is rejected

So the the drug stays in the system for more than 397 minutes

To learn more about mean and Standard Deviation, refer to the link

https://brainly.com/question/28225633

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