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vovikov84 [41]
2 years ago
13

Twenty nine concrete blocks were sampled and tested for crushing strength in order to estimate the proportion that were sufficie

ntly strong for a certain application. Twenty seven of the 29 blocks were sufficiently strong. Use the small-sample method to construct a 95% confidence interval for the proportion of blocks that are sufficiently strong.
Mathematics
1 answer:
Vitek1552 [10]2 years ago
4 0

Answer:

<em>95% confidence interval for the proportion of blocks that are sufficiently strong</em>

<em>(0.83913 , 1.02293)</em>

Step-by-step explanation:

<u><em>Step:-1</em></u>

Given that the sample size 'n' = 29 blocks

<em>Estimate proportion </em>

                       p = \frac{x}{n} = \frac{27}{29} = 0.93103

<u><em>Step:-2</em></u>

<em>95% confidence interval for the proportion of blocks that are sufficiently strong</em>

(p^{-} -Z_{0.05} \sqrt{\frac{p(1-p)}{n} }  , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} } )

(0.93103 -1.96 \sqrt{\frac{0.93103(1-0.93103)}{29} }  , 0.93103 + 1.96 \sqrt{\frac{0.93103(1-0.93103)}{29} } )

(0.93103 -  0.0919 , 0.93103 +0.0919)

(0.83913 , 1.02293)

<u><em>Final answer</em></u>:-

<em>95% confidence interval for the proportion of blocks that are sufficiently strong</em>

<em>(0.83913 , 1.02293)</em>

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