Question

Activity 2: Hypothesis test from start to finish

Is there evidence of a negative correlation between systolic blood pressure and heart rate? In a sample of 200 patients, we found a sample correlation of -0.057.

1. State the hypotheses of interest.

H₀: rho=0    rho<0

2. What is the notation and value of the sample statistic?

r

3. Use StatKey to generate a randomization distribution for these hypotheses. Use the data set ‘ICU Admissions’ available on StatKey.

What is the p-value?

0.211

4. Which two of the options below are correct interpretations of the p-value (insert your calculated p-value from (3) in the blank):
   1. If there is no linear association between systolic blood pressure and heart rate in the population, the chance of seeing a sample correlation of -0.057 or less is _______________.
   2. If there is a negative linear association between systolic blood pressure and heart rate, the chance of seeing a sample correlation of -0.057 or less is _____________.
   3. If there is no linear association between systolic blood pressure and heart rate in the population, the proportion of samples with a sample correlation of -0.057 or less is _______.
   4. If there is a negative linear association between systolic blood pressure and heart rate, the proportion of samples with a sample correlation of -0.057 or less is _______________.

5. What is the formal conclusion at a significance level of 0.05?

6. What is the conclusion in context?

7. Based on the p-value you calculated in part 3, what would the correct formal conclusion be if we were testing a two-sided hypothesis with the same sample?

1. Reject H₀ and accept Ha
2. Reject Ha and accept H₀
3. Fail to reject H₀
4. Fail to reject Ha

Answer 1

Null and alternative hypothesis:

Ho: ρ = 0 ; Ha: ρ < 0

Notation = r

Correlation, r = -0.0570

Test statistic :  

t = r*√(n-2)/√(1-r²) = -0.057 *√(200 - 2)/√(1 - (-0.057)²) = -0.8034

df = n-2 = 198

p-value = T.DIST(-0.8034, 198, 1) = 0.2114

Answer: B If there is no linear association between systolic blood pressure and heart rate in the population, the proportion of samples with a sample correlation of -0.057 or less is 0.2114

Conclusion:

Answer : C. Fail to reject Ho