It is known that 34% of parcels packed on a production line have damaged outer packaging. A new packing procedure is introduced, and the manager believes that this proportion has decreased.
A random sample of 50 parcels packed under the new procedure is taken, and X X\,X is the number with damaged outer packaging. A test is to be carried out at the 5% significance level.
Let p p\,p be the population proportion of parcels with damaged outer packaging under the new procedure. The null hypothesis is H0H_0H0: p=0.34p=0.34p=0.34.
State the alternative hypothesis.
Find the critical region for this test.
Find the actual significance level of a test based on this critical region.
In the sample, 10 parcels have damaged outer packaging. State the conclusion in context.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.