A chemical engineer is investigating whether a new catalyst increases the yield of a specific synthetic reaction. The yield, measured in grams per batch, is denoted by yyy. A random sample of 80 batches produced without the catalyst (Group 1) and an independent random sample of 120 batches produced with the catalyst (Group 2) were recorded. The results are summarized in the table below:
| Sample Group | Sample Size | ∑y\sum y∑y | ∑y2\sum y^2∑y2 | Unbiased estimate of mean | Unbiased estimate of variance |
|---|---|---|---|---|---|
| Without catalyst | 80 | 6240 | 492000 | yˉ1\bar{y}_1yˉ1 | s12s_1^2s12 |
| With catalyst | 120 | — | — | 81.5 | 380.4 |
Calculate the values of yˉ1\bar{y}_1yˉ1 and s12s_1^2s12.
Test, at the 1% level of significance, whether there is evidence that the mean yield is greater when the catalyst is used. State your hypotheses clearly.
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.