Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-sl/hypothesis-testing/13-4-8/problems/

jmaths

IB Mathematics: Applications and Interpretation SL · 13.4: Hypothesis Testing · 13.4.8

Hypothesis testing: exam review Exam review Answers

Section A: short questions

    1. (a) \(H_0:\mu=500\), \(H_1:\mu<500\), where \(\mu\) is the population mean mass of a box of cereal, in grams
    2. (b) Unusual; reject H0. There is sufficient evidence that the mean mass of a box is less than 500 g.
    1. (a) H0: the proportions are 0.4, 0.3, 0.2, 0.1; H1: they are not
    2. (b) 80, 60, 40, 20
    3. (c) 3
    4. (d) χ² = 12.3, p = 0.00642
    5. (e) Reject H0: there is sufficient evidence, at the 5% significance level, that the proportions of the drinks chosen are not as the café states
    1. (a) 5
    2. (b) 11.1
    3. (c) Reject H0: there is sufficient evidence, at the 5% significance level, that the die is not fair
    4. (d) 0.0122
    1. (a) \(H_0:\mu=1000\), \(H_1:\mu<1000\), where \(\mu\) is the population mean mass of a bag of sugar, in grams
    2. (b) the masses of the bags are normally distributed
    3. (c) mean \(=995\), \(s_{n-1}=4.70\)
    4. (d) t = −3.10, p = 0.00638
    5. (e) Reject H0: there is sufficient evidence, at the 5% significance level, that the mean mass of a bag of sugar is less than 1000 g
    1. (a) Both populations are normally distributed; the population variances are equal
    2. (b) \(H_0:\mu_1=\mu_2\), \(H_1:\mu_1\ne\mu_2\), where \(\mu_1\) and \(\mu_2\) are the population mean masses of tubs from machine 1 and machine 2, in grams
    3. (c) 25
    4. (d) t = 2.84, p = 0.00881
    5. (e) Reject H0: there is sufficient evidence, at the 5% significance level, that the mean masses of tubs from the two machines are different
    1. (a) Judge 1: 2, 4, 1, 6, 7, 3, 8, 5; judge 2: 1, 6, 2, 5, 7, 3, 8, 4 (for A to H)
    2. (b) 0.905
    3. (c) \(H_0\): no correlation between the judges' ranks; \(H_1\): positive correlation
    4. (d) Reject H0: there is sufficient evidence, at the 5% significance level, that the judges tend to agree

Section B: long questions

    1. (a) \(H_0\): \(X\sim B(4,0.15)\)
    2. (b) 83.5, 59.0, 15.6, 1.84, 0.081
    3. (c) The expected frequencies for X = 3 and X = 4 are below 5
    4. (d) 3 groups, so 2
    5. (e) χ² = 10.8, p = 0.00456
    6. (f) Reject H0: there is sufficient evidence, at the 5% significance level, that the number of faulty batteries in a pack does not follow B(4, 0.15)
    7. (g) X = 2 or more: more than expected (observed 28, expected 17.5)
    1. (a) H0: music preference is independent of year group; H1: it is not
    2. (b) (2−1)(3−1) = 2
    3. (c) 89 × 63 ÷ 166 = 33.8
    4. (d) χ² = 14.2, p = 8.29 × 10⁻⁴
    5. (e) Reject H0: there is sufficient evidence, at the 5% significance level, that music preference is not independent of year group
    6. (f) Year 10, Hip-hop: observed 13, expected 24.1 (fewer than expected)
    7. (g) Reject H0 at 1%
    1. (a) ranks of the values of \(x\): 1, 2, 3, 4.5, 4.5, 6, 7, 8, 9, 10; ranks of the values of \(y\): 10, 8, 9, 6, 5, 7, 3, 4, 2, 1
    2. (b) −0.936
    3. (c) \(H_0\): no correlation; \(H_1\): negative correlation
    4. (d) Reject H0: there is sufficient evidence, at the 5% significance level, that more time on social media goes with less sleep
    5. (e) r_s = −0.936: a strong negative association; students who spend more time on social media tend to sleep less
    6. (f) No change: 6.0 is still the largest value of x, so the ranks do not change
    7. (g) No change: the order of the values does not change

jmaths.xyz · AI SL · 13.4.8 Unit review