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Question

It is desired to test $H_0: \mu=75$ against $H_{\mathrm{a}}: \mu<75$ using $\alpha=.10$. The population in question is uniformly distributed with standard deviation 15. A random sample of size 49 will be drawn from the population. Describe the (approximate) sampling distribution of $\bar{x}$ under the assumption that $H_0$ is true.

Solution

VerifiedAnswered 11 months ago

Answered 11 months ago

The sampling distribution of $x̄$ is approximately normal because the sample size is large (as per central limit theorem). The population mean is $(μ = 75)$ and the $σ_x̄$ is $2.14$.

The calculation for $σ_x̄$ is shown below:

$\begin{aligned} σ_x̄&= \dfrac{15}{\sqrt{49}}\\ \\ &= \boxed{2.14}\\ \end{aligned}$

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