Question

Donna wants to test whether or not drinking coffee will immediately increase heart rate while sitting in class. Six people measured their heart rates before drinking coffee and then the same six people took their heart rates after drinking their coffee. Please calculate the t-statistic for this experiment; then state the critical value; then come to a conclusion concerning the null hypothesis; and then state what the implications are concerning drinking coffee.

No Coffee                   Coffee

79                                  84

71                                  78

84                                  87

66                                  75

74                                  80

76                                  82

Answer 1

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: Drinking coffee will not immediately increase heart rate while sitting in class.

Alternative hypothesis: H_a: Drinking coffee will immediately increase heart rate while sitting in class.

H₀: µ_d = 0 versus H_a: µ_d < 0

This is a left tailed or lower tailed test.

We take difference as the ‘No coffee’ minus ‘Coffee’.

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

µ_d = 0

Dbar = -6

S_d = 2

n = 6

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (-6 - 0)/[2/sqrt(6)]

t = -7.3485

df = n – 1 = 6 - 1 = 5

α = 0.05

The p-value by using t-table is given as below:

P-value = 0.0004

P-value < α

So, we reject the null hypothesis

There is sufficient evidence to conclude that drinking coffee will immediately increase heart rate while sitting in class.