A construction company notes the time, $$$t$$$ days, that it takes to build each house of a certain design. The results for a random sample of 60 such houses are summarised as follows. $$$ \Sigma t=4820 \quad \Sigma t^{2}=392050 $$$ Calculate a $$$98 \%$$$ confidence interval for the population mean time. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_62 Year：2021 Question No：1(a)

Answer:

$\operatorname{Est}(\mu)=\frac{4820}{60}$ or $\frac{241}{3}$ or $80.3(3 \mathrm{sf})$
$\operatorname{Est}\left(\sigma^{2}\right)=\frac{60}{59}\left(\frac{392050}{60}-\left(\frac{4820}{60}\right)^{2}\right)$
$82.0904\left(\frac{14530}{177}\right)$ to $82.635$ or $\mathrm{SD}=9.0604$ to $9.0904(3 \mathrm{sf})$
$z=2.326$
$\frac{4820}{60} \pm z \times \sqrt{\frac{82.0904^{\prime}}{60}}$
$77.6$ to $83.1(3 \mathrm{sf})$

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’.)

6.4.8 determine, from a large sample, an approximate confidence interval for a population proportion.

Answer:

Knowledge points:

Solution:

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