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IB Mathematics: Applications and Interpretation HL · 13.4: Hypothesis Testing · 13.4.21

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Exam question practice Problem set A

Show each probability as a calculator step. Name the distribution before using it.

Difficulty: first skills applying them stretch

Skills

  1. The mass, X grams, of a baguette is normally distributed with mean 260 and standard deviation 10. Find the probability that

    1. (a) one baguette has a mass greater than 272 g;
    2. (b) two baguettes chosen at random both have a mass greater than 272 g.

  2. The mass, X grams, of a baguette is normally distributed with mean 260 and standard deviation 10. Two baguettes are chosen at random. Find the probability that their total mass is greater than 540 g.

  3. A bakery changes its flour, which increases the mass of every baguette by 2%. Before the change the mass has mean 260 g and standard deviation 10 g.

    1. (a) Find the new mean.
    2. (b) Find the new standard deviation.

In context

  1. A baker thinks that a new recipe has increased the mean mass of a baguette. The old mean was 260 g and the standard deviation is 10 g. She tests a random sample of 16 baguettes at the 5% significance level.

    1. (a) State the null and alternative hypotheses.
    2. (b) Find the critical region for the sample mean. Give the critical value to 3 significant figures.

  2. The new recipe in fact increases the mass of every baguette by 2%. A test of H0: μ = 260 against H1: μ > 260 uses a sample of 16 baguettes, a standard deviation of 10 g and a 5% significance level. Before the change the mean mass is 260 g.

    1. (a) Find the probability of a Type II error. Use the unrounded critical value.

Stretch

  1. The mass, X grams, of a baguette is normally distributed with mean 260 and standard deviation 10. A baker changes the recipe and thinks the mean mass has increased. She tests this at the 5% significance level, using a random sample of 16 baguettes.

    1. (a) Find the probability that a baguette has a mass greater than 272 g.
    2. (b) Two baguettes are chosen at random. Find the probability that their total mass is greater than 540 g.
    3. (c) State the null and alternative hypotheses.
    4. (d) Find the critical region for the sample mean.
    5. (e) The new recipe in fact makes every baguette 2% heavier. Find the new mean and standard deviation of the mass of a baguette.
    6. (f) Find the probability of a Type II error. Use the unrounded critical value.

jmaths.xyz · AI HL · 13.4.21 Exam question: sums of normals, a test for a mean and Type II error