Answer:
We conclude that the population mean is not equal to 17.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 17
Sample mean, [tex]\bar{x}[/tex] = 14.12
Sample size, n = 40
Alpha, α = 0.05
Population standard deviation, σ = 4
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 17\\H_A: \mu \neq 17[/tex]
We use Two-tailed z test to perform this hypothesis.
a) 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{14.12 - 17}{\frac{4}{\sqrt{40}} } = -4.5536[/tex]
b) P-value can be calculated from the standard z-table.
P-value = 0.0000
c) Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17
d) Now, [tex]z_{critical} \text{ at 0.05 level of significance } = \pm 1.96[/tex]
e) Rejection Rule:
We reject the null hypothesis if it is less than lower critical value and greater than the upper critical value
If the z-statistic lies outside the acceptance region which is from -1.96 to +1.96, we reject the null hypothesis.
f) Since the calculated z-stat lies outside the acceptance region, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17.
