The probability that a fair spinner lands on 3 is 14\displaystyle \frac1441.
In 12 spins, find the probability of exactly two 3s and the probability of more than four 3s. Alex then believes the probability is greater than 14\displaystyle \frac1441 after 15 of 40 spins are 3s. For part (b), use H0:p=14\displaystyle H_0:p=\frac14H0:p=41, H1:p>14\displaystyle H_1:p>\frac14H1:p>41 and Y∼B(40,14)\displaystyle Y\sim B(40,\frac14)Y∼B(40,41) under H0H_0H0.
Calculate the exact p-value.
State the decision at the 5% level and give a conclusion in context.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.