Edexcel S3 2024 January — Question 6

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Year2024
SessionJanuary
TopicHypothesis test of a normal distribution

  1. A random sample of 8 three-month-old golden retriever dogs is taken.
The heights of the golden retrievers are recorded.
Using this sample, a 95\% confidence interval for the mean height, in cm, of three-month-old golden retrievers is found to be \(( 45.72,53.88 )\)
  1. Find a 99\% confidence interval for the mean height. You may assume that the heights are normally distributed with known population standard deviation. Some summary statistics for the weights, \(x \mathrm {~kg}\), of this sample are given below. $$\sum x = 91.2 \quad \sum x ^ { 2 } = 1145.16 \quad n = 8$$
  2. Calculate unbiased estimates of the mean and the variance of the weights of three-month-old golden retrievers. A further random sample of 24 three-month-old golden retrievers is taken. The unbiased estimates of the mean and the variance of the weights, in kg , from this sample are found to be 10.8 and 17.64 respectively.
  3. Estimate the standard error of the mean weight for the combined sample of 32 three-month-old golden retrievers.