Question

Consider a population proportion p = 0.68. a-1. Calculate the expected value and the standard error of P− with n = 30. (Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.) a-2. Is it appropriate to use the normal distribution approximation for P− ? Yes No b-1. Calculate the expected value and the standard error of P− with n = 40. (Round "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.) b-2. Is it appropriate to use the normal distribution approximation for P− ?

Answer 1

Answer:

a) Expected value = 20.4, Standard error = 0.085

b) Yes

c) Expected value = 27.2, Standard error = 0.073

d) Yes

Step-by-step explanation:

We are given the following in the question:

Population proportion, p = 0.68

a) expected value and the standard error

Sample size, n = 30

$E(x) = np = 30\times 0.68 = 20.4$

$\text{Standard error} = \sqrt{\dfrac{p(1-p)}{n}} = \sqrt{\dfrac{0.68(1-0.68)}{30}} = 0.085$

b) Yes it is appropriate to use normal approximation as:

$np = 30\times 0.68 = 20.4 > 5\\n(1-p) = 30\times (1-0.68) = 9.6 > 5$

c) expected value and the standard error

Sample size, n = 40

$E(x) = np = 40\times 0.68 = 27.2$

$\text{Standard error} = \sqrt{\dfrac{p(1-p)}{n}} = \sqrt{\dfrac{0.68(1-0.68)}{40}} = 0.0773$

b) Yes it is appropriate to use normal approximation as:

$np = 40\times 0.68 = 27.2> 5\\n(1-p) = 40\times (1-0.68) = 12.8 > 5$