A tea company sells boxes of tea bags with a stated weight of 125 g. A consumer watchdog suspects that the mean weight of these boxes is less than the stated weight. They weigh a random sample of 80 boxes and find the weights have a mean of 123.5 g and a standard deviation of 4.2 g.
Using a 1% level of significance, test whether or not the watchdog's suspicion is justified. State your hypotheses clearly.
Find the 95% confidence interval for the mean weight of a tea box from this production line.
Based on your findings, state the advice that should be given to the tea company regarding the weight of their boxes.
The tea company upgrades their machinery, resulting in a new mean weight μ\muμ and a reduced standard deviation of 2.5 g. Assume that individual box weights are normally distributed. A researcher takes a sample of size nnn and uses the sample mean Xˉ\bar{X}Xˉ as an estimator of μ\muμ.
Find the minimum value of nnn such that P(∣Xˉ−μ∣<0.5)≥0.99P(|\bar{X} - \mu| < 0.5) \ge 0.99P(∣Xˉ−μ∣<0.5)≥0.99.
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.