1. Many coffee drinkers say that they experience an increase in heart rate after consuming a cup of coffee. A sample of 4 people had their resting heart rate measured, were given 300 ml of coffee to drink, and then ten minutes later had their heart rate measured again. The data from these samples is given in the chart below.

Heart Rate before: 68, 75, 93, 77

Heart rate After: 74, 81, 96, 82

Perform a paired-samples t-test, with a p level of 0.05 to determine if the persons mean heart rate does increase after ingesting coffee.

a) If Population 1 is defined as the heart rates after ingesting coffee and Population 2 is defined as the heart rates before ingesting coffee, define u1 and u2.

b) State the null and alternative hypothesis, and if this is two-tailed, right-tailed, or left tailed test

c) Use the following to help determine the mean of the difference scores (d) and the standard deviation:

d) Find t95 , that is find the cut-off(s) for a p level of 0.05

e) Find the value of the -test statistic(s), and show it in a diagram relative to t95

f) Conclude on your findings, both generally and specifically to this problem

g) Using the information from the sample of 4 people, give the 90% confidence interval for the population mean difference in heart rate.