Question

5) A researcher at the University of Michigan medical school believes that coffee consumption may increase heart rate. Suppose it is known that heart rate (in beats per minute) is normally distributed with an average of 70 bpm for adults. A random sample of 24 adults was selected and it was found that their average heartbeat was 73 bpm after coffee consumption, with a standard deviation of 7 bpm. Is there any evidence to support the researcher’s belief at 2.5% level of significance? a) State the appropriate null and alternate hypotheses. b) What assumptions are you making on the population distribution? c) Compute the value of the test statistic and its P-value. d) State your conclusion.

Answer 1

Given,

X_bar = 73

s = 7

n = 24

Significance level = 0.025

1) Hypothesis :

H0: = 70

H1:  70

2) test statistic Z value

t = (x_bar - ​​​​​​) /(s/n)

= (73-70)/(7/24)

t = 2.0996

3) Df = n-1 = 24-1 =23

p value for t test statistic with 23 degrees of freedom is 0.0469

4) conclusion:

P value (0.0469) is greater than significance level. Hence do not reject null hypothesis. There sufficient evidence to conclude the average is 70 bpm for adults.