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/b/

jmaths

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

Hypothesis testing: exam review Exam review: second paper Answers

Section A: short questions

    1. (a) \(H_0:\mu=90\), \(H_1:\mu>90\), where \(\mu\) is the population mean charging time of a tablet, in minutes
    2. (b) Not unusual; do not reject H0. There is insufficient evidence that the mean charging time is greater than 90 minutes.
    1. (a) H0: the types are in the ratio 9 : 3 : 3 : 1; H1: they are not
    2. (b) 180, 60, 60, 20
    3. (c) 3
    4. (d) χ² = 1.09, p = 0.780
    5. (e) Do not reject H0: there is insufficient evidence, at the 5% significance level, that the seed types are not in the ratio 9 : 3 : 3 : 1
    1. (a) 7
    2. (b) 18.5
    3. (c) Do not reject H0: there is insufficient evidence, at the 1% significance level, that the spinner is not fair
    4. (d) 0.172
    1. (a) \(H_0:\mu=40\), \(H_1:\mu<40\), where \(\mu\) is the population mean time to answer a call, in seconds
    2. (b) the times to answer a call are normally distributed
    3. (c) mean \(=39.4\), \(s_{n-1}=2.06\)
    4. (d) t = −1.02, p = 0.165
    5. (e) Do not reject H0: there is insufficient evidence, at the 5% significance level, that the mean time to answer a call is less than 40 seconds
    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 test scores of students using method 1 and method 2
    3. (c) 22
    4. (d) t = 1.34, p = 0.195
    5. (e) Do not reject H0: there is insufficient evidence, at the 5% significance level, that the mean scores using the two methods are different
    1. (a) Taster 1: 4, 1, 7, 3, 5, 8, 2, 6; taster 2: 2, 4, 5, 1, 6, 8, 7, 3 (for A to H)
    2. (b) 0.333
    3. (c) \(H_0\): no correlation between the tasters' ranks; \(H_1\): positive correlation
    4. (d) Do not reject H0: there is insufficient evidence, at the 5% significance level, that the tasters tend to agree

Section B: long questions

    1. (a) \(H_0\): \(X\sim B(4,\frac{1}{6})\)
    2. (b) 193, 154, 46.3, 6.17, 0.309
    3. (c) The expected frequency for X = 4 is below 5
    4. (d) 4 groups, so 3
    5. (e) χ² = 0.990, p = 0.804
    6. (f) Do not reject H0: there is insufficient evidence, at the 5% significance level, that the number of sixes in a turn does not follow B(4, 1/6)
    7. (g) X = 3 or more: more than expected (observed 8, expected 6.48)
    1. (a) H0: arriving late is independent of the way a student travels; H1: it is not
    2. (b) (3−1)(2−1) = 2
    3. (c) 48 × 62 ÷ 154 = 19.3
    4. (d) χ² = 1.45, p = 0.485
    5. (e) Do not reject H0: there is insufficient evidence, at the 5% significance level, that arriving late is not independent of the way a student travels
    6. (f) Walking, Late: observed 16, expected 19.3 (fewer than expected)
    7. (g) Do not reject H0 at 1%
    1. (a) ranks of the values of \(x\): 1, 2, 3, 4, 5.5, 5.5, 7, 8, 9; ranks of the values of \(y\): 3.5, 6, 9, 3.5, 8, 1, 5, 7, 2
    2. (b) −0.168
    3. (c) \(H_0\): no correlation; \(H_1\): negative correlation
    4. (d) Do not reject H0: there is insufficient evidence, at the 5% significance level, that rent is lower further from the centre
    5. (e) r_s = −0.168: a weak negative association; rent tends to fall slightly with distance, but the link is weak
    6. (f) No change: 16.0 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