Moderate -0.3 This is a straightforward one-tailed binomial hypothesis test with clearly stated context. Students must identify H₀: p=0.5, H₁: p>0.5, find P(X≥21) under B(30,0.5), and compare to 5%. The setup is standard S2 material with no conceptual tricks, though it requires careful probability calculation and correct interpretation of the one-tailed test.
2. David claims that the weather forecasts produced by local radio are no better than those achieved by tossing a fair coin and predicting rain if a head is obtained or no rain if a tail is obtained. He records the weather for 30 randomly selected days. The local radio forecast is correct on 21 of these days.
Test David's claim at the \(5 \%\) level of significance.
State your hypotheses clearly.
So significant / reject \(H_0\) / In Critical Region
M1 dep
Dependent on 2nd M1
Evidence to suggest David's claim is incorrect or weather forecast produced by local radio is better than those achieved by tossing/flipping a coin
A1
Correct contextualised statement. Do not allow non-contextual conflicting statements e.g. "significant" and "accept \(H_0\)"
# Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0: p = 0.5$ | B1 | |
| $H_1: p > 0.5$ | B1 | SC: If both hypotheses correct but different letter to $p$ used: B1B0. If no letter used: B0B0 |
| $X \sim B(30, 0.5)$ | M1 | Using correct Binomial |
| $P(X \geq 21) = 1 - P(X \leq 20)$ or $P(X \leq 19) = 0.9506$ or $P(X \geq 20) = 0.0494$ | M1 | One tail: writing or using $1 - P(X \leq 20)$ |
| $= 1 - 0.9786 = 0.0214$ | A1 | CR $X \geq 20$ |
| So significant / reject $H_0$ / In Critical Region | M1 dep | Dependent on 2nd M1 |
| Evidence to suggest **David's claim is incorrect** or weather **forecast** produced by local **radio** is better than those achieved by **tossing/flipping a coin** | A1 | Correct contextualised statement. Do not allow non-contextual conflicting statements e.g. "significant" and "accept $H_0$" |
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2. David claims that the weather forecasts produced by local radio are no better than those achieved by tossing a fair coin and predicting rain if a head is obtained or no rain if a tail is obtained. He records the weather for 30 randomly selected days. The local radio forecast is correct on 21 of these days.
Test David's claim at the $5 \%$ level of significance.
State your hypotheses clearly.\\
\hfill \mbox{\textit{Edexcel S2 2012 Q2 [7]}}