Question

A researcher investigates whether daily exercise decreases long-term stress levels. On a national survey, the mean stress level of those who do not exercise is 8.5. The stress score rating is 0 to 10, whereby higher scores are associated with higher stress levels. The researcher recruited nine (9) participants who exercised daily for two weeks and recorded the following stress scores:

5 ,  3 , 8 , 3 , 7 , 4 , 5 , 6 , 4

Showing calculations where necessary:

a) State the null and the alternative hypotheses

b) Calculate the t obtained value

c) What is the number of df?

d) Let a represent alpha symbol. Using a = 0.05, determine t critical value and interpret the results

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

(a)

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: Daily exercises do not decrease long-term stress level.

Alternative hypothesis: H_a: Daily exercises decrease long-term stress level.

H₀: µ = 8.5 versus H_a: µ < 8.5

This is a lower tailed test.

(b)

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 8.5

Xbar = 5

S = 1.732050808

n = 9

t = (Xbar - µ)/[S/sqrt(n)]

t = (5 - 8.5)/[ 1.732050808/sqrt(9)]

t = -6.0622

(c)

We have

df = n – 1

df = 9 - 1 = 8

(d)

We are given

α = 0.05

Critical value = -1.8595

(by using t-table or excel)

Test statistic t < critical value

So, we reject the null hypothesis

There is sufficient evidence to conclude that Daily exercises decrease long-term stress level.