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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.