Question

a poll conducted by the uc berkeley institute of governmental studies in 2019 found that 51.7% of 4527 respondents said they considered moving out of the state. complete parts a through c.
a) compute a c (50.3 %, 53.2 (type integers
b) interpret you (type integers
yes
no
therefore, all of the conditions are satisfied, so a normal model can be used to calculate the confidence interval. a confidence interval can be calculated using technology or the formula shown below where (hat{p}) is the sample proportion and (z^*) is the critical value found using technology or a table. the standard error formula is needed to calculate the confidence interval, where (hat{p}) is the proportion of successes in the sample, (hat{q} = 1 - hat{p}) is the proportion of failures in the sample, and (n) is the sample size. for the purpose of this example, technology will be used.
one is (hat{p} pm z^* \times se(hat{p})) where (se(hat{p}) = sqrt{\frac{hat{p}hat{q}}{n}})
one is
c) since high c it can be reaso use technology to calculate the confidence interval. remember that the sample size, (n), is 4527 and the confidence level is 95%.
(type integers or decimals rounded to three decimal places as needed.)
since the confi

Explanation:

Step1: Identify key values

$\hat{p} = 0.517$, $n = 4527$, $z^* = 1.96$ (for 95% confidence)

Step2: Calculate standard error

$$SE(\hat{p}) = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = \sqrt{\frac{0.517 \times 0.483}{4527}} \approx 0.00745$$

Step3: Compute margin of error

$$ME = z^* \times SE(\hat{p}) = 1.96 \times 0.00745 \approx 0.0146$$

Step4: Find confidence interval

$$\hat{p} \pm ME = 0.517 \pm 0.0146$$
Lower bound: $0.517 - 0.0146 = 0.5024$
Upper bound: $0.517 + 0.0146 = 0.5316$

Step5: Round to 3 decimals

Convert to percentages and round: $50.2\%$, $53.2\%$

Answer:

a) $(50.2, 53.2)$
b) Yes
c) We are 95% confident that the true proportion of people in the state who considered moving out is between 50.2% and 53.2%.