A quality control engineer monitors the failure torque of a specialized structural bolt. Historically, the failure torque is normally distributed with a mean of 45.0 Nm and a standard deviation of 1.8 Nm. The engineer believes a new heat treatment has increased the mean failure torque.
A random sample of 8 bolts is tested. The hypothesis test is conducted at the 2.5% level of significance, with:
H0:μ=45.0 H_0: \mu = 45.0 H0:μ=45.0 H1:μ>45.0 H_1: \mu > 45.0 H1:μ>45.0One measurement is accidentally erased from the log. The seven remaining measurements, in Nm, are:
46.2,44.8,47.1,45.5,46.8,45.9,44.2 46.2, \quad 44.8, \quad 47.1, \quad 45.5, \quad 46.8, \quad 45.9, \quad 44.2 46.2,44.8,47.1,45.5,46.8,45.9,44.2The engineer correctly concludes that there is sufficient evidence to reject the null hypothesis at the 2.5% level. Calculate the minimum possible value of the missing measurement. 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.