| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2006 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Moderate -0.3 This is a straightforward S3 confidence interval question requiring standard calculations: sample mean and variance from data, then a routine confidence interval using known σ and z-values. Part (c) tests basic understanding of confidence level interpretation. All steps are textbook procedures with no problem-solving or novel insight required, making it slightly easier than average. |
| Spec | 5.05b Unbiased estimates: of population mean and variance5.05d Confidence intervals: using normal distribution |
3. The drying times of paint can be assumed to be normally distributed. A paint manufacturer paints 10 test areas with a new paint. The following drying times, to the nearest minute, were recorded.
$$82 , \quad 98 , \quad 140 , \quad 110 , \quad 90 , \quad 125 , \quad 150 , \quad 130 , \quad 70 , \quad 110 .$$
\begin{enumerate}[label=(\alph*)]
\item Calculate unbiased estimates for the mean and the variance of the population of drying times of this paint.
Given that the population standard deviation is 25 ,
\item find a 95\% confidence interval for the mean drying time of this paint.
Fifteen similar sets of tests are done and the $95 \%$ confidence interval is determined for each set.
\item Estimate the expected number of these 15 intervals that will enclose the true value of the population mean $\mu$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2006 Q3 [12]}}