Respuesta :
Answer:
P-value = 0.02275
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 12 kilograms
Sample mean, [tex]\bar{x}[/tex] = 11.5 kilograms
Sample size, n = 4
Alpha, α = 0.05
Population standard deviation, σ = 0.5 kilograms
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 12\\H_A: \mu < 12[/tex]
We use one-tailed(left) 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{11.5 - 12}{\frac{0.5}{\sqrt{4}} } = -2[/tex]
We calculate the p-value from the standard z-table:
P-value = 0.02275
The p-value of the hypothsis 0.00135
Data;
- Standard deviation = 0.5kg
- mean elongation = 12kg
- n = 4
- Mean = 11.5
Null and Alternative Hypothesis
[tex]H_-o : \mu =12\\H_1 : \mu < 12[/tex]
Since the standard deviation = 0.5
Mean = 11.25, n = 4
Test statistic =
[tex]t = \frac{x -\mu}{\sigma / \sqrt{n} } \\t = \frac{11.25-12}{0.5/\sqrt{4} } \\t = -3[/tex]
The p-value = p(z < -3) = 0.00135
The p-value of the hypothsis 0.00135
Learn more on p-value here;
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