The chance that a webpage visitor clicks a link is 0.15. Angela believes that increasing the link's font size increases the click probability. After the change, 20 of a random sample of 90 visitors click.
Use H0:p=0.15H_0:p=0.15H0:p=0.15, H1:p>0.15 H_1:p>0.15\,H1:p>0.15 and, under H0H_0H0, X∼B(90,0.15)X\sim B(90,0.15)X∼B(90,0.15).
Explain why an upper-tailed test is appropriate.
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.