A researcher at the University of Washington medical school

A researcher at the University of Washington medical school believes that energy drink 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 25 adults was selected and it was found that their average heartbeat was 73 bpm after energy drink consumption, with a standard deviation of 7 bpm.

Formulate the null and alternative hypotheses.

Test the hypotheses in the previous question at the 10% significance level to determine if we can infer that energy drink consumption increases heart rate.

Solution

To test the nulll hypothesis

H₀ : Energy consumption does not increase heart rate i.e mu = 70

against

H₁ : Energy consumption increase heart rate i.e mu > 70 ( right tailed test)

Under the null hypothesis the test statistics is

Cal Z = (Xbar - mu₀) * sqrt(n) / sigma = (73 - 70) * 5 / 7 = 15/7 = 2.1429

Tab Z at 0.1 los = 1.29

As Cal Z > Tab Z we will reject null hypothesis and conclude that energy drink consumption increases heart rate.