DP Further Mathematics HL Questionbank

• Syllabus

3.6

Sub sections and their related questions

Null and alternative hypotheses, \({H_0}\) and \({H_1}\) .

• 11M.1.hl.TZ0.1a: Bottles of iced tea are supposed to contain 500 ml. A random sample of 8 bottles was selected and...
• 09M.2.hl.TZ0.1B.a: State and justify an appropriate test procedure giving the null and alternate hypotheses.
• 09M.2.hl.TZ0.1B.b: What is the critical region for the sample mean if the probability of a Type I error is to be...
• 09M.2.hl.TZ0.1B.c: If the mean weight of the bags is actually \(28\).1 kg, what would be the probability of a Type...
• 07M.2.hl.TZ0.2b: An automatic machine is used to fill bottles of water. The amount delivered, \(Y\) ml , may be...
• 12M.1.hl.TZ0.5a: The shopkeeper claims that when one of the coins is tossed, the probability of obtaining a head...
• SPNone.2.hl.TZ0.2b: The farm manager claims that the mean weight of apples is \(100\) grams but the buyer from the...
• 15M.1.hl.TZ0.14: Sarah is the quality control manager for the Stronger Steel Corporation which makes steel sheets....
• 15M.2.hl.TZ0.2c: Test, at the \(1\%\) level of significance, the null hypothesis \(\mu  = 35\) against the...
• 18M.1.hl.TZ0.7a: An investigator wishes to test the hypotheses H0 : μ = 65, H1 : μ > 65. He decides on the...
• 18M.1.hl.TZ0.7b.i: She decides to use the same acceptance criteria as the previous investigator. Find the...
• 18M.1.hl.TZ0.7b.ii: Find the critical value for \({\bar x}\) if she wants the probabilities of a Type I error and a...
• 18M.1.hl.TZ0.14b: The null hypothesis μ = 46.5 is tested against the alternative hypothesis μ < 46.5 at the λ%...

Significance level.

• 15M.2.hl.TZ0.2c: Test, at the \(1\%\) level of significance, the null hypothesis \(\mu  = 35\) against the...
• 18M.1.hl.TZ0.7a: An investigator wishes to test the hypotheses H0 : μ = 65, H1 : μ > 65. He decides on the...
• 18M.1.hl.TZ0.7b.i: She decides to use the same acceptance criteria as the previous investigator. Find the...
• 18M.1.hl.TZ0.7b.ii: Find the critical value for \({\bar x}\) if she wants the probabilities of a Type I error and a...
• 18M.1.hl.TZ0.14b: The null hypothesis μ = 46.5 is tested against the alternative hypothesis μ < 46.5 at the λ%...

Critical regions, critical values, \(p\)-values, one-tailed and two-tailed tests.

• 15M.1.hl.TZ0.14: Sarah is the quality control manager for the Stronger Steel Corporation which makes steel sheets....
• 15M.2.hl.TZ0.2c: Test, at the \(1\%\) level of significance, the null hypothesis \(\mu  = 35\) against the...
• 18M.1.hl.TZ0.7a: An investigator wishes to test the hypotheses H0 : μ = 65, H1 : μ > 65. He decides on the...
• 18M.1.hl.TZ0.7b.i: She decides to use the same acceptance criteria as the previous investigator. Find the...
• 18M.1.hl.TZ0.7b.ii: Find the critical value for \({\bar x}\) if she wants the probabilities of a Type I error and a...
• 18M.1.hl.TZ0.14b: The null hypothesis μ = 46.5 is tested against the alternative hypothesis μ < 46.5 at the λ%...

Type I and II errors, including calculations of their probabilities.

• 15M.1.hl.TZ0.14: Sarah is the quality control manager for the Stronger Steel Corporation which makes steel sheets....
• 18M.1.hl.TZ0.7a: An investigator wishes to test the hypotheses H0 : μ = 65, H1 : μ > 65. He decides on the...
• 18M.1.hl.TZ0.7b.i: She decides to use the same acceptance criteria as the previous investigator. Find the...
• 18M.1.hl.TZ0.7b.ii: Find the critical value for \({\bar x}\) if she wants the probabilities of a Type I error and a...
• 18M.1.hl.TZ0.14b: The null hypothesis μ = 46.5 is tested against the alternative hypothesis μ < 46.5 at the λ%...

Testing hypotheses for the mean of a normal population.

• 15M.2.hl.TZ0.2c: Test, at the \(1\%\) level of significance, the null hypothesis \(\mu  = 35\) against the...
• 16M.1.hl.TZ0.4a: State suitable hypotheses.
• 16M.1.hl.TZ0.4b: (i)     Give a reason why a \(t\) test is appropriate and write down its degrees of...
• 16M.1.hl.TZ0.4c: (i)     Find unbiased estimates of \(\mu \) and \({\sigma ^2}\). (ii)     Find the value of the...
• 16M.1.hl.TZ0.4d: State the conclusions that the president of the club should reach from this test, giving reasons...
• 18M.1.hl.TZ0.7a: An investigator wishes to test the hypotheses H0 : μ = 65, H1 : μ > 65. He decides on the...
• 18M.1.hl.TZ0.7b.i: She decides to use the same acceptance criteria as the previous investigator. Find the...
• 18M.1.hl.TZ0.7b.ii: Find the critical value for \({\bar x}\) if she wants the probabilities of a Type I error and a...
• 18M.1.hl.TZ0.14b: The null hypothesis μ = 46.5 is tested against the alternative hypothesis μ < 46.5 at the λ%...