The operational endurance of a random sample of 15 'Volt-X' industrial sensors is measured under standard load. The mean endurance of the sample is recorded as 118.4 hours118.4\text{ hours}118.4 hours. The endurance times of these sensors are known to follow a normal distribution.
Given that the population standard deviation for these sensors is 4.2 hours4.2\text{ hours}4.2 hours,
estimate the limits between which 95%95\%95% of the endurance times of individual sensors lie.
find a 98%98\%98% confidence interval for the mean endurance time of the 'Volt-X' sensors.
A quality control engineer claims that the true mean endurance time of these sensors is 121.5 hours121.5\text{ hours}121.5 hours.
Comment on the engineer's claim. Give a reason for your answer.
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.