Answer:
Null hypothesis
Alternative hypothesis
t = - 2.05
Degree of freedom df = 14
P-value = 0.0298
Decision rule: To reject if significance level ∝ is greater than P-value.
Conclusion: We reject at the level of significance ∝ = 0.1, thus there is sufficient evidence to conclude that the machine is underfilling the bags.
Step-by-step explanation:
Given that:
Population mean = 443
Sample size n = 15
Sample mean = 434
standard deviation = 17
Level of significance ∝ = 0.01
The null and the alternative hypothesis can be computed as:
Null hypothesis
Alternative hypothesis
The t-test statistics can be computed as :
t = - 2.05
Degree of freedom df = n - 1
Degree of freedom df = 15 - 1
Degree of freedom df = 14
From t distribution table; from the area in the lower tail to the left of t = -2.05 and for the degree of freedom df = 14, it is given by 0.0298
Thus, P-value = 0.0298
Decision rule: To reject if significance level ∝ is greater than P-value.
Conclusion: We reject at the level of significance ∝ = 0.1, thus there is sufficient evidence to conclude that the machine is underfilling the bags.