Question

MIS445- Discussion Topic:

Confidence intervals and p-values are commonly used in business decision making. Using the CSU-Global Library, identify at least two business journals (or articles) that have used confidence intervals and/or p-values. For each journal (or article), describe:

1. the problem statement
2. the parameter(s) of interest
3. the conclusion and/or decision.  

In addition, state the sample size. If they are using a confidence interval, state the confidence level and margin of error. If they are using the p-value, state the hypotheses, p-value, and level of significance.

Answer 1

A confidence interval is a range of population values with which the sample data are compatible. A significance test considers the likelihood that the sample data has come from a particular hypothesised population.

The 95% confidence interval consists of all values less than 1.96 standard errors away from the sample value, testing against any population value in this interval will lead to p > 0.05. Testing against values outside the 95% confidence interval (which are more than 1.96 standard errors away) will lead to p-values < 0.05.

Similarly, the 99% confidence interval consists of all values less than 2.58 standard errors away from the sample value, testing against any hypothesised population value in this interval will give a p-value > 0.01. Testing against values outside the 99% confidence interval (which are more than 2.58 standard errors away) will lead to p-values < 0.01. In general:

1) The mean birthweight of 53 CMV infected babies was 3060.75g (standard deviation = 601.03g, standard error = 82.57g).

A 95% confidence interval for the population mean birthweight of CMV infected babies is therefore given by:

(3060.75 ± 1.96(82.57)) = (2898.91, 3222.59g)

Similarly, the 99% confidence interval for the mean is:

(3060.75 ± 2.58(82.57)) = (2847.72, 3273.78g)

We are 95% confident that the true mean is somewhere between 2898.91 and 3222.59g, testing against values outside this range will lead to p-values < 0.05.

We are 99% confident that the true mean is between 2847.72 and 3273.78g (notice that this is a wider interval, we are more confident that it contains the population mean). Testing against values within this range will lead to p-values > 0.01.

The test given previously showed that the sample mean was significantly different from a hypothesised population mean of 3263.57g. The p-value for that test was 0.014 and this corresponds to the hypothesised population mean of 3263.57g lying outside the 95% confidence interval but inside the 99%.

2) A sample of 33 boys with recurrent infections have their diastolic blood pressures measured. Their mean blood pressure is 62.5 mmHg, standard deviation 8.2.

Using the sample standard deviation to estimate the population standard deviation, samples of size 33 will be distributed with standard error:

Therefore, a 99% confidence interval for the mean diastolic blood pressure of boys with recurrent infections is (62.5 ± 2.58(1.43)) = (58.81, 66.18mmHg).

We wish to know whether boys with recurrent infections are different from boys in general who are known to have pressures of on average 58.5mmHg. The null hypothesis to be tested is that the 33 boys come from a population with a mean dbp of 58.5mmHg.

The observed sample mean is 62.5 - 58.5/ 1.43 = 2.797 standard errors away from the hypothesised mean of 58.5mmHg.

Consulting the table of the normal distribution, we find 0.002 < p < 0.01. Using the linked spreadsheet we get the exact p-value of 0.005, a sample with a mean 4mmHg away from the hypothesised value would occur by chance one time in 200 (5 in 1000).

The 99% confidence interval does not contain the hypothesised mean and p < 0.01 as expected.