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.
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.