OCR S3 2016 June — Question 3 8 marks

Exam BoardOCR
ModuleS3 (Statistics 3)
Year2016
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConfidence intervals
TypeCalculate CI for proportion
DifficultyModerate -0.3 This is a straightforward two-part confidence interval question requiring standard formulas. Part (i) uses the normal approximation for a proportion with given sample data. Part (ii) applies the normal distribution confidence interval formula for a mean with known variance. Both are routine S3 calculations with no conceptual challenges, making it slightly easier than average.
Spec5.05d Confidence intervals: using normal distribution

3
  1. A company packages butter. Of 50 randomly selected packs, 8 were found to have damaged wrappers. Find an approximate \(95 \%\) confidence interval for the proportion of packs with damaged wrappers.
  2. The mass of a pack has a normal distribution with standard deviation 8.5 g . In a random sample of 10 packs the masses, in g , are as follows. $$\begin{array} { l l l l l l l l l l } 220 & 225 & 218 & 223 & 224 & 220 & 229 & 228 & 226 & 228 \end{array}$$ Find a 99\% confidence interval for the mean mass of a pack.

3 (i) A company packages butter. Of 50 randomly selected packs, 8 were found to have damaged wrappers. Find an approximate $95 \%$ confidence interval for the proportion of packs with damaged wrappers.\\
(ii) The mass of a pack has a normal distribution with standard deviation 8.5 g . In a random sample of 10 packs the masses, in g , are as follows.

$$\begin{array} { l l l l l l l l l l } 
220 & 225 & 218 & 223 & 224 & 220 & 229 & 228 & 226 & 228
\end{array}$$

Find a 99\% confidence interval for the mean mass of a pack.

\hfill \mbox{\textit{OCR S3 2016 Q3 [8]}}