The phenomenon of bottle flipping has hit the nation. You design a machine that

Question

The phenomenon of bottle flipping has hit the nation. You design a machine that can randomly flip a ttle. You observe 2270 random, independent flips, and 343 land the correct way. Estimate the overall proportion of bottles that land correctly when flipped randomly. Use a 99% confidence level a) State the parameter of interest. Verify that the necessary conditions are present in order to carry out the procedure. b) Find the critical value and standard error Critical Value: c) Find the confidence interval: d) Interpret the 99% confidence interval in context Standard Error:

Explanation / Answer

a) Sample proportion p = 343/2270 = 0.1511
Nomality condition : np = 2270*0.1511 = 343 > 5
and nq = 2270*(1-0.1511) = 1927 >5
Therefore, the given data follows normal distribution

b) Critical value = ±2.5758
Standard Error = Sqrt(pq/n) = sqrt(0.1511*0.8489/2270) = 0.007517

c) 99% confidence interval :
p +/- Z1% SE(p) = (0.1511 - 2.5758*0.007517,0.1511 + 2.5758*0.007517)
=(0.13174, 0.17046)

d) The 99% chance that the population proportion would be lies between 0.13174 and 0.1706

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