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.
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.