A national survey shows that 95% of year 12 students use social media. Arvin suspects that the percentage of year 12 students at his college who use social media is less than the national percentage. He chooses a random sample of 20 students at his college and notes the number who use social media. He then carries out a test at the 2% significance level.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

1. [M1] P(X ≤ n) (n ≤ 20) attempted, using B(20, 0.95); OE
2. [M1] P(X < 17) or P(X ≤ 16) attempted, using B(20, 0.95); OE
3. [A1] (P(X < 17)) = 0.0755 and (P(X ≤ 16)) = 0.0159; OE (0.925 and 0.984) both correct
4. [A1] Rej region is X ≤ 16 or X < 17; Dependent on M1M1 and previous answers correct to at least 0.075/0.076 and 0.016 or 0.92/0.93 and 0.98; Correct unsupported answers of 0.0755 and 0.0159 OE scores M1 M1 A0
5. [B1] 0.0159; FT their rejection region, from Binomial in a, if P(X in rejection region) < 0.025
6. [M1] Use of B(20, 0.7)
7. [M1] P(X > 16 | p = 0.7); Correct method using B(20, 0.7)
8. [A1] = 0.107