A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the drug, 21 subjects had a mean wake time of 97.5 min and a standard deviation of 44.1 min. Assume that the 21 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is effective?

So on this case the 95% confidence interval would be given by (77.426;117.574)    

Assuming this previous info:Before treatment with zopiclone, 21 subjects  had a mean wake time of 102.8 min

Since the lower bound for the confidence interval is lower than 102.8 we don't have enough evidence to conclude that we have a significant effect.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s=44.2 represent the sample standard deviation

n=21 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,20)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (77.426;117.574)    

Assuming this previous info:Before treatment with zopiclone, 21 subjects  had a mean wake time of 102.8 min

Since the lower bound for the confidence interval is lower than 102.8 we don't have enough evidence to conclude that we have a significant effect.

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.

d. you cannot tell because there are no values shown.