Answer:
Test: [tex]\mu[/tex] < 20 with normal distⁿ
Hypothesis test:
H0: [tex]\mu \ge[/tex] 20 (Null Hypothesis, H₀ : [tex]\mu[/tex] = 20 is also correct)
H1: [tex]\mu[/tex] < 20 (Alternative Hypothesis, also called H₁)
This is lower tailed test.
Since sample is large, sample standard deviation can be taken as an approximation of population standard deviation.
x = 19.3
[tex]\sigma[/tex] = 11.1
n = 444
significance level, [tex]\alpha[/tex] = 0.05 (If no value is given, we take level of 0.05)
Test statistic [tex]z* = \frac{x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]= \frac{19.3-20}{11.1/\sqrt{444}}[/tex]
= - 1.33
The attached files contains additional information
