At 0.01 significance level the hypothesis is rejected.
Null Hypothesis (H₀): The sample data occurs purely from chance.
Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.
If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.
Given that,
x = 28
s = 2.9
μ = 31
n = 8
α = 0.01
Then, the Null Hypothesis : H₀ = 31
The Alternate Hypothesis : H₁ < 31
The average number of cigeratte smoker per day is less than 31.
Test Statistics:
t = x -μ / s√n
= 28 - 31/ 2.9√8
= -3/ 8.41
= -0.356
Since the p-value of 0.0046 is less than the significance level of 0.01, the auditor rejects the null hypothesis.
