Hypothesis Testing (Normal Distribution) (A Level only) (Edexcel A-Level Mathematics): Quizzes

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Sample Mean Distribution
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If XN(μ,σ2)X \sim N(\mu, \sigma^2) with sample size nn, what is the distribution of Xˉ\bar{X}?

N(μ,σ2n)N\left(\mu, \frac{\sigma^2}{n}\right)

For XN(50,42)X \sim N(50, 4^2) with sample size 16, what is the variance of Xˉ\bar{X}?

11

What does the null hypothesis H0H_0 represent in hypothesis testing?

No change in mean (default position)

Testing if fertilizer increases mean height. Which alternative hypothesis is correct?

H1:μ>21H_1: \mu > 21

For a two-tailed test at 5% significance, what % is at each tail?

2.5%2.5\%

What is the critical/rejection region?

Where we reject H0H_0 if observation lies

One-tailed test, 5% level, P(Xˉ>21.2)=0.0334P(\bar{X} > 21.2) = 0.0334. What is the decision?

Reject H0H_0 (0.0334 < 0.05)

When defining the parameter being tested, which symbol must be used?

μ\mu

Testing H0:μ=5H_0: \mu = 5 vs H1:μ5H_1: \mu \neq 5. Which distribution to use?

XˉN(5,σ2n)\bar{X} \sim N\left(5, \frac{\sigma^2}{n}\right)

What is the probability calculation in Method 2 sometimes called?

p-value

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