A study measured the LDL cholesterol level in 49 subjects. The subjects were then treated with raw garlic for six months. The mean change in the 49 subjects was a reduction of 0.4 with a standard deviation of 21.0 (assume this is the actual standard deviation for the population, not and estimate). Find a 95% confidence interval for the mean change in LDL cholesterol after a treatment of garlic. Do you think garlic is effective in reducing LDL cholesterol? Source: Article by Gardner, et al., from Archives of Internal Medicine, Vol. 167.

So on this case the 95% confidence interval would be given by (-6.28;5.48)    For this case since the confidence interval contains the 0 we don't have enough evidence to conclude that the garlic is effective reducing the LDL cholesterol

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".

Let X the random variable who represent the mean change in the LDL

represent the sample mean

population mean (variable of interest)

represent the population standard deviation

n=49 represent the sample size  

Solution to the problem

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

  (1)

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: "=-NORM.INV(0.025,0,1)".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 (-6.28;5.48)    For this case since the confidence interval contains the 0 we don't have enough evidence to conclude that the garlic is effective reducing the LDL cholesterol