Answer:
We conclude that mean diameter is not equal to 15 µm.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 15
Sample mean, [tex]\bar{x}[/tex] = 15.2
Sample size, n = 87
Alpha, α = 0.05
Sample standard deviation, σ = 1.8
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 15\\H_A: \mu \neq 15[/tex]
We use Two-tailed t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n-1}} }[/tex] Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{15.2-15}{\frac{1.8}{\sqrt{86}} } = 1.03[/tex]
Now,
[tex]t_{critical} \text{ at 0.05 level of significance, 86 degree of freedom } = \pm 1.9879[/tex]
Since,
[tex]|t_{stat}| < |t_{critical}|[/tex]
We reject the null hypothesis and fail to accept it.
P-value is 0.3
Since p-value < 0.05
We reject the null hypothesis and accept the alternate hypothesis and conclude that mean diameter is not equal to 15 µm.
Both the approaches that the that mean diameter is not equal to 15 µm.
