An agricultural scientist is monitoring the yield of a specific variety of wheat. The yield per hectare is normally distributed with a standard deviation of 4.8 kg4.8\text{ kg}4.8 kg. Traditionally, the mean yield, μ\muμ, is known to be 190 kg190\text{ kg}190 kg.
The scientist suspects that a new fertilizer has increased the mean yield. She collects data from a random sample of 666 hectares and performs a hypothesis test at the 10%10\%10% significance level.
She tests H0:μ=190H_0: \mu = 190H0:μ=190 against H1:μ>190H_1: \mu > 190H1:μ>190.
When reviewing her notes, she finds that she has lost one of the recordings. The five available recordings are:
192.5,188.2,197.6,191.4,195.3 192.5, \quad 188.2, \quad 197.6, \quad 191.4, \quad 195.3 192.5,188.2,197.6,191.4,195.3Given that the result of the hypothesis test was to reject the null hypothesis H0H_0H0 at the 10%10\%10% level of significance, calculate the minimum possible value of the missing measurement, xxx. Give your answer correct to 1 decimal place.
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.