Consider a population proportion p 026 a1 Calculate the sta

Consider a population proportion p = 0.26. a-1. Calculate the standard error for the sampling distribution of the sample proportion approximately normal with n = 19 and n = 64? (Do not round intermediate calculations. Round your answers to 4 decimal places.) Standard error a-2. Is the sampling distribution of the sample proportion approximately normal with n = 19 and n = 64? Approximately Normal b. Can you use the normal approximation to calculate the probability that the sample proportion is between 0.24 and 0.26 for both sample sizes? Approximately Normal

Solution

(a-1) standard error =sqrt(p*(1-p)/n)

=sqrt(0.26*(1-0.26)/19)

=0.1006

standard error =sqrt(p*(1-p)/n)

=sqrt(0.26*(1-0.26)/64)

=0.0548

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(a-2)

For n=19, No

For n=64, Yes

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(b)P(0.24<phat<0.26)

= P((0.24-0.26)/sqrt(0.26*(1-0.26)/19) <(phat-p)/sqrt(p*(1-p)/n)<(0.26-0.26)/sqrt(0.26*(1-0.26)/19))

=P(-0.20<Z<0) =0.0793 (from standard normal table)

P(0.24<phat<0.26)

= P((0.24-0.26)/sqrt(0.26*(1-0.26)/64) <(phat-p)/sqrt(p*(1-p)/n)<(0.26-0.26)/sqrt(0.26*(1-0.26)/64))

=P(-0.36<Z<0) =0.1406 (from standard normal table)