Sample Mean Distribution (AQA A-Level Mathematics): Quizzes

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

σ2n\frac{\sigma^2}{n}

For X∼N(100,7)X \sim N(100, 7) with sample size 60, what is the distribution of Xˉ\bar{X}?

N(100,760)N\left(100, \frac{7}{60}\right)

If H1:μ>21H_1: \mu > 21, what type of test is this?

One-tailed test

What does H0H_0 represent in hypothesis testing?

No change in mean (default position)

What happens if the observation lies in the critical region?

Reject H0H_0

For a 5% one-tailed test, if P(Xˉ>21.2)=0.2755P(\bar{X} > 21.2) = 0.2755, what do we conclude?

Accept H0H_0 (0.2755 > 0.05)

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

2.5%

What does 'Accept H0H_0' mean in the context of the fertilizer test?

Insufficient evidence for the claim

If H0:μ=5H_0: \mu = 5, what value of μ\mu should be used in the test distribution?

5

What is the probability calculation method sometimes referred to as?

P-value

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