Question

2 Systolic Blood Pressure & Heart Rate

Researchers want to know if there is a relationship between systolic blood pressure and heart rate in the population of all ICU patients. They collected data from a sample of 200 ICU patients and computed a correlation of r = -0.057 between systolic blood pressure and heart rate. StatKey was used to construct a 95% confidence interval of [-0.212, 0.098] for the population correlation.

1. If researchers wanted to conduct a hypothesis test to determine if there is a relationship between systolic blood pressure and heart rate in the population of ICU patients, what hypotheses would they test? State the null and alternative hypotheses that should be used. [10 points]

2. If the hypotheses from part a were tested, would you expect the p value to be less than or greater than 0.05? Explain why. [10 points]

Hint: Apply the 95% confidence interval given in the scenario

3 House Prices in Canton, NY

Research question: Is the mean price of a house in Canton, New York different from $160,000?

Data were collected from a sample of 10 homes and StatKey was used to conduct a randomization test. A p value of 0.688 was computed for the two-tailed test.

1. In order to increase statistical power should the researchers obtain a larger or smaller sample size? [5 points]

2. In addition to changing the sample size, as in part a, what is one other change that could be made in future studies to increase the statistical power of this test? [5 points]

Answer 1

a.

Null hypothesis H0: The linear correlation between systolic blood pressure and heart rate in the population of ICU patients is 0. That is, = 0.

Alternative hypothesis H0: The linear correlation between systolic blood pressure and heart rate in the population of ICU patients is not 0. That is, 0.

b.

Since the 95% confidence interval of correlation contains the value 0, there is no significant evidence that the linear correlation between systolic blood pressure and heart rate in the population of ICU patients is not 0 and thus we fail to reject the null hypothesis and we expect p value to be greater than 0.05.

3.

a.

The large sample size would reduce the standard error of mean and hence the probability to reject the null hypothesis (power) will increase when the null hypothesis is false.

In order to increase statistical power, the researchers should obtain a larger sample size.

b.

A large power will have low Type II error. For a low type II error, there should be high Type I error (Significance level ).

Thus, in addition to changing the sample size, significance level can be increased to increase the statistical power of this test.