Confidence interval

When checking the use-by date of a specific type of canned meat in warehouses of meat industry products, 340 canned goods were randomly selected, and it was found that 63 of them had passed their warranty period. Establish a 95% confidence interval to estimate the percentage of canned goods past the warranty period.

Correct answer:

a =  0.144
b =  0.2266

Step-by-step explanation:

$$\begin{gathered} n_1=340 \\ {n}_2=63 \\ z=1.96 \\ \mu =\frac{n_2}{n_1}=\frac{63}{340}\doteq 0.1853 \\ \alpha =95\%=\frac{95}{100}=\frac{19}{20}=0.95 \\ e=\sqrt{\frac{\mu \cdot (1-\mu )}{n_1}}=\sqrt{\frac{0.1853\cdot (1-0.1853)}{340}}\doteq 0.0211 \\ a=\mu -z\cdot e=0.1853-1.96\cdot 0.0211=0.144 \end{gathered}$$

$b=\mu +z\cdot e=0.1853+1.96\cdot 0.0211=0.2266$

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