Suzanne is a member of a sports club - AQA - A-Level Maths Mechanics - Question 17 - 2018 - Paper 3

To investigate this claim, we first state the hypotheses:

• Null Hypothesis, $H_0$: The probability of winning a match with the new racket is the same as before, $p = 0.5$.
• Alternative Hypothesis, $H_1$: The probability of winning a match with the new racket is different, $p \neq 0.5$.

Next, we will use the Binomial distribution model, with the number of matches played ( n = 10 ) and the number of wins ( k = 7 ). Using the binomial probability formula:

$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$

The probabilities we are interested in are $P(X \leq 6)$ and $P(X \geq 7)$, which we calculate separately.

1. Calculate $P(X \leq 6)$:

   • Using cumulative binomial tables or a calculator, we find: $P(X \leq 6) = 1 - P(X \geq 7)$
   • This gives us $P(X \leq 6) \approx 0.8281$ or $0.172$.

2. Compare this result with the significance level of 0.10:

   • Since $P(X \geq 7)$ is roughly $0.172$, and $0.172 > 0.10$, we do not reject the null hypothesis.

Conclusion: There is insufficient evidence that Suzanne's new racket has made a difference.