A random sample of 75 students at a large college was selected for a survey. 15 of these students said that they owned a car. From this result an approximate $$\(\alpha \%\)$$ confidence interval for the proportion of all students at the college who own a car was calculated. The width of this interval was found to be $$\(0.162\)$$. Calculate the value of $$\(\alpha\)$$ correct to 2 significant figures. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w21_qp_63 Year：2021 Question No：3
Answer:
est \((\mathrm{p})=0.2\) accept \(\frac{15}{75}\)
\(2 \times z \times \sqrt{\frac{0.2 \times 0.8}{75}}=0.162\)
\(z\left[=0.081 \times \sqrt{\frac{75}{0.2 \times 0.8}}\right]=1.754\)
\(\Phi\left(' 1.754^{\prime}\right)=0.96[03]\)
' \(0.96^{\prime}-\left(1-10.96^{\prime}\right)\)
\(\alpha=92\)
\(2 \times z \times \sqrt{\frac{0.2 \times 0.8}{75}}=0.162\)
\(z\left[=0.081 \times \sqrt{\frac{75}{0.2 \times 0.8}}\right]=1.754\)
\(\Phi\left(' 1.754^{\prime}\right)=0.96[03]\)
' \(0.96^{\prime}-\left(1-10.96^{\prime}\right)\)
\(\alpha=92\)
Knowledge points:
6.4.8 determine, from a large sample, an approximate confidence interval for a population proportion.
Solution:
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