Hypothesis tests: past paper questions

Real questions on hypothesis tests

The newest 20 of 145 written questions. Open one to see it on the real paper.

1. 9709/61 · October/November 2025 · Q2[8]
   The mean mass of packets of Trueleaf tea is supposed to be 500 grams. An inspector wishes to test whether this value is correct. He weighs 60 randomly chosen packets and notes the mass, $x$ grams, of each packet. The results are summarised as follows. $n=60\sum x=29970\sum x^2=14970300$ Test, at t...See it on the paper →
2. 9709/61 · October/November 2025 · Q5a[4]
   It is known that $20\%$ of households in a certain country contain more than 4 people. Laxmi believes that, in her town, the percentage is lower than $20\%$. She chooses a random sample of 40 households in her town and notes the number which contain more than 4 people. She then carries out a test at the $2.5\%$ signifi...See it on the paper →
3. 9709/61 · October/November 2025 · Q5b[1]
   It is known that $20\%$ of households in a certain country contain more than 4 people. Laxmi believes that, in her town, the percentage is lower than $20\%$. She chooses a random sample of 40 households in her town and notes the number which contain more than 4 people. She then carries out a test at the $2.5\%$ signifi...See it on the paper →
4. 9709/61 · October/November 2025 · Q5c[1]
   It is known that $20\%$ of households in a certain country contain more than 4 people. Laxmi believes that, in her town, the percentage is lower than $20\%$. She chooses a random sample of 40 households in her town and notes the number which contain more than 4 people. She then carries out a test at the $2.5\%$ signifi...See it on the paper →
5. 9709/62 · October/November 2025 · Q4a[6]
   An inspector believes that $18\%$ of cups made at a certain factory contain flaws. The factory owner claims that the true percentage is less than $18\%$. The inspector examines a random sample of $40$ cups and finds that $3$ of them contain flaws. (a) Stating a necessary assumption, use a binomial distribution to test...See it on the paper →
6. 9709/62 · October/November 2025 · Q6a[6]
   The weekly profit, in dollars, made by a certain firm has a normal distribution. In the past, the weekly profit had the distribution $\text{N}(736,26^2)$. Following a change in management, the mean weekly profit for 35 randomly chosen weeks is $725$. (a) Stating a necessary assumption, test at the 2% significance leve...See it on the paper →
7. 9709/62 · October/November 2025 · Q6b[1]
   The weekly profit, in dollars, made by a certain firm has a normal distribution. In the past, the weekly profit had the distribution $\text{N}(736,26^2)$. Following a change in management, the mean weekly profit for 35 randomly chosen weeks is $725$. (b) State the probability of a Type I error.See it on the paper →
8. 9709/62 · October/November 2025 · Q6c[5]
   The weekly profit, in dollars, made by a certain firm has a normal distribution. In the past, the weekly profit had the distribution $\text{N}(736,26^2)$. Following a change in management, the mean weekly profit for 35 randomly chosen weeks is $725$. (c) Given that the mean weekly profit is now in fact $718$, find the...See it on the paper →
9. 9709/63 · October/November 2025 · Q2[8]
   The mean mass of packets of Trueleaf tea is supposed to be 500 grams. An inspector wishes to test whether this value is correct. He weighs 60 randomly chosen packets and notes the mass, $x$ grams, of each packet. The results are summarised as follows. $n=60\sum x=29970\sum x^2=14970300$ Test, at...See it on the paper →
10. 9709/63 · October/November 2025 · Q5a[4]
    It is known that $20\%$ of households in a certain country contain more than 4 people. Laxmi believes that, in her town, the percentage is lower than $20\%$. She chooses a random sample of 40 households in her town and notes the number which contain more than 4 people. She then carries out a test at the $2.5\%$ signifi...See it on the paper →
11. 9709/63 · October/November 2025 · Q5b[1]
    It is known that $20\%$ of households in a certain country contain more than 4 people. Laxmi believes that, in her town, the percentage is lower than $20\%$. She chooses a random sample of 40 households in her town and notes the number which contain more than 4 people. She then carries out a test at the $2.5\%$ signifi...See it on the paper →
12. 9709/63 · October/November 2025 · Q5c[1]
    It is known that $20\%$ of households in a certain country contain more than 4 people. Laxmi believes that, in her town, the percentage is lower than $20\%$. She chooses a random sample of 40 households in her town and notes the number which contain more than 4 people. She then carries out a test at the $2.5\%$ signifi...See it on the paper →
13. 9709/61 · May/June 2025 · Q3b[5]
    The time, $T$ minutes, for a certain daily bus journey is normally distributed. The bus company claims that the mean of $T$ is 45. A passenger believes that the mean of $T$ is actually greater than 45. She notes the times taken for this journey on a random sample of 60 days. The results are summarised below. $n = 60 \...See it on the paper →
14. 9709/61 · May/June 2025 · Q5a(ii)[6]
    (a) The random variables $W$ and $X$ have the independent distributions Po(1.2) and Po(2.3) respectively. (ii) Use a suitable approximation to find $P(S>600)$.See it on the paper →
15. 9709/61 · May/June 2025 · Q6a[1]
    A manufacturer of cell phones claims that 25% of students own a Pumpkin phone. Jeyeraj thinks that the proportion of students at his large college who own a Pumpkin phone is less than 25%. He plans to test the manufacturer’s claim. He chooses a random sample of 30 students at his college. If the number of students who...See it on the paper →
16. 9709/61 · May/June 2025 · Q6b[3]
    A manufacturer of cell phones claims that 25% of students own a Pumpkin phone. Jeyeraj thinks that the proportion of students at his large college who own a Pumpkin phone is less than 25%. He plans to test the manufacturer’s claim. He chooses a random sample of 30 students at his college. If the number of students who...See it on the paper →
17. 9709/62 · May/June 2025 · Q5[4]
    The amount of time, in minutes, spent by a customer on one visit to a certain shop is modelled by the random variable $X\sim N(\mu ,{\sigma }^2)$. In the past, the values of $\mu$ and $\sigma$ were 10.5 and 3.8 respectively. The shop has recently moved to a new location, and the manager hopes that the new value of $\mu$...See it on the paper →
18. 9709/62 · May/June 2025 · Q8a[5]
    Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, $p$, that it will show a six on one throw is less than $\frac{1}{6}$. She throws the dice 30 times and finds that it shows a six on exactly 2 throws. (a) Use a binomial distribution with a 5% significance level to test Birgitte...See it on the paper →
19. 9709/62 · May/June 2025 · Q8b[2]
    Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, $p$, that it will show a six on one throw is less than $\frac{1}{6}$. She throws the dice 30 times and finds that it shows a six on exactly 2 throws. (b) Calculate the probability of a Type I error.See it on the paper →
20. 9709/62 · May/June 2025 · Q8c[3]
    Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, $p$, that it will show a six on one throw is less than $\frac{1}{6}$. She throws the dice 30 times and finds that it shows a six on exactly 2 throws. (c) Given that the value of $p$ is actually 0.02, calculate the probability...See it on the paper →

What examiners said

The hypothesis test was reasonably well attempted, with the null and alternative hypotheses generally correctly stated. The most common error noted was the omission of √𝟔𝟎 in the denominator when standardising, and premature approximation of 14.44 to 14.4 caused a loss of accuracy for some candidates. After standardising to find z, a clear comparison was required and a common error for those who c...

— Examiner report, February/March 2025, 9709/62 Q2(b) (Cambridge)

Many candidates correctly calculated P(X ≤ 3) using B(35, 0.2). It was important that the full Binomial expression was shown here. An acceptable significance level was then required, and this was often successfully given. In general candidates made a good attempt at this question.

— Examiner report, February/March 2025, 9709/62 Q5(a) (Cambridge)

Many candidates realised that the probability of a Type I error was 0.0605 as calculated in 5(a).

— Examiner report, February/March 2025, 9709/62 Q5(b) (Cambridge)