written 5.1 years ago by
teamques10
★ 65k
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modified 5.1 years ago
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Solution:
$\bar{X}=103.75$
$\mu=108.75$
$(X_{i}-\bar{X})=843.75$ and $n=16$
Calculate standard deviation,
$s^{2}=\cfrac{\sum(X_{i}-\bar{X})^{2}}{n}=\cfrac{843.75}{16}=52.73$
Step 1: The null hypothesis $H_{0}=\mu=108.75$
Alternative hypothesis $H_{a}=\mu \ne 108.75$
Step 2: Calculation of the test statistic.
$t=\cfrac{\bar{X}-\mu}{s/\sqrt{n-1}}= \cfrac{103.75-108.75}{\sqrt{52.74}/\sqrt{16-1}} = \cfrac{-5}{1.875} = -2.67$
$\therefore |t| = |-2.67|=2.67$
Step 3: Level of significance = 5%
i.e., $\alpha=0.05$
Step 4: Critical …
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