Variance of a Normal distribution and the F-test

Variance of a Normal distribution and the F-test Quiz

Spec 6.1–2 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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1. A sample of $n=21$ has $s^2=5$ . For $H_0:\sigma^2=4$ , the test statistic is
- A. $25$
- B. $26.25$
- C. $1.25$
- D. $21$
2. The degrees of freedom of the $\chi^2$ distribution for a sample of size $12$ are
- A. $12$
- B. $13$
- C. $11$
- D. $10$
3. For a $90\%$ confidence interval for $\sigma^2$ , the upper $\chi^2$ point gives
- A. the upper limit of the interval
- B. the lower limit of the interval
- C. the sample variance
- D. the test statistic
4. $s_1^2=20$ with $n_1=11$ and $s_2^2=8$ with $n_2=16$ . The $F$ statistic with larger variance on top has degrees of freedom
- A. $(15,\ 10)$
- B. $(11,\ 16)$
- C. $(16,\ 11)$
- D. $(10,\ 15)$
5. For a two-tailed F-test at the $5\%$ level, the critical value is the upper
- A. $5\%$ point
- B. $2.5\%$ point
- C. $10\%$ point
- D. $50\%$ point