In the past, the mean time taken by Freda for a particular daily journey was $$\(39.2\)$$ minutes. Following the introduction of a one-way system, Freda wishes to test whether the mean time for the journey has decreased. She notes the times, $$\(t\)$$ minutes, for 40 randomly chosen journeys and summarises the results as follows. Calculate unbiased estimates of the population mean and variance of the new journey time.
Exam No：9709_m20_qp_62 Year：2020 Question No：3(a)
Answer:
\(\operatorname{est}(\mu)=37.6\) or \(\frac{1504}{40}\) or \(\frac{188}{5}\)
\[
\operatorname{est}\left(\sigma^{2}\right)=\frac{40}{39}\left[\frac{57760}{40}-37.6^{2}\right]=31.0154=\frac{2016}{65}
\]
\[
=31 .(0)(3 \mathrm{sf})
\]
\[
\operatorname{est}\left(\sigma^{2}\right)=\frac{40}{39}\left[\frac{57760}{40}-37.6^{2}\right]=31.0154=\frac{2016}{65}
\]
\[
=31 .(0)(3 \mathrm{sf})
\]
Knowledge points:
6.4.6 calculate unbiased estimates of the population mean and variance from a sample, using either raw or summarised data (Only a simple understanding of the term ‘unbiased’ is required, e.g. that although individual estimates will vary the process gives an accurate result ‘on average’.)
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download