Specialist Mathematics · Unit 4 · Statistical inference · Confidence intervals for means
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A researcher collects data on the reaction times (in milliseconds) of drivers in a large population. A random sample of 36 drivers yields a sample mean reaction time of 215 ms with a sample standard deviation of 18 ms. Which of the following correctly represents the approximate 95% confidence interval for the population mean reaction time?
A pharmaceutical company tests the effectiveness of a new pain relief medication. A random sample of 36 patients is selected, and their pain relief response times (in minutes) are recorded. The sample mean is found to be \(\bar{x} = 18.2\) minutes with a sample standard deviation of \(s = 4.8\) minutes. (a) Determine a 95% confidence interval for the population mean response time. (2 marks) (b) The manufacturer claims the mean response time is 16.5 minutes. Comment on the reasonableness of this claim based on your confidence interval. (2 marks)
A researcher measures the heights of a random sample of 25 adult males from a large population. The sample has a mean height of 178.5 cm and a standard deviation of 6.2 cm. The researcher calculates a 95% confidence interval for the population mean height as (176.0, 181.0) cm. Determine whether this confidence interval is reasonable by: (i) verifying whether the sample mean lies within the interval (ii) checking whether the margin of error is consistent with a 95% confidence level for the given sample.
A veterinary researcher collects a random sample of 45 dogs from a large animal shelter to estimate the mean weight of all dogs at the shelter. The sample yields a mean weight of 18.6 kg with a sample standard deviation of 3.2 kg. Use the information in the stimulus to construct a 95% confidence interval for the population mean weight.
A student investigating online shopping habits surveys a random sample of 64 customers. The sample mean time spent per week shopping online is 5.2 hours with a sample standard deviation of 1.8 hours. Using this data, determine a 95% confidence interval for the population mean time spent shopping online per week. Give your answer to 1 decimal place.