Respuesta :
Answer:
We reject the null hypothesis and accept the alternate hypothesis. Thus, it be concluded that the population mean is less than 20.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 60
Sample mean, [tex]\bar{x}[/tex] = 19.5
Sample size, n = 60
Alpha, α = 0.05
Population standard deviation, σ = 1.8
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 20\\H_A: \mu < 20[/tex]
We use One-tailed z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{19.5 - 20}{\frac{1.8}{\sqrt{60}} } = -2.151[/tex]
Now, [tex]z_{critical} \text{ at 0.05 level of significance } = -1.64[/tex]
Since,
[tex]z_{stat} < z_{critical}[/tex]
We reject the null hypothesis and accept the alternate hypothesis. Thus, it be concluded that the population mean is less than 20.
