Respuesta :
Answer:
(a) The best point estimate of population proportion is, [tex]\hat p=0.28[/tex].
(b) The margin of error is 0.018.
(c) The 95% confidence interval for population proportion is (0.262, 0.298).
Step-by-step explanation:
In a random sample of n = 2625 US adults, X = 735 agree with statement "only one true love for each person".
The sample proportion of US adults who agrees is: [tex]\hat p=\frac{X}{n} =\frac{735}{2625}= 0.28[/tex]
The standard error is given to be, [tex]SE_{\hat p}=0.009[/tex]
(a)
A point estimate is the numerical value that can be used to estimate the population parameter value. It is computed using the sample values.
The point estimate of population proportion of US adults who agree is given by the sample proportion.
[tex]p=\hat p=0.28[/tex]
Thus, the best point estimate of population proportion is, [tex]\hat p=0.28[/tex].
(b)
The margin of error for a 95% confidence interval of population proportion is:
[tex]MOE=z_{\alpha /2}\times SE_{\hat p}[/tex]
For a 95% confidence interval the critical value is:
[tex]z_{\alpha /2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table for the critical value.
Compute the MOE as follows:
[tex]MOE=z_{\alpha /2}\times SE_{\hat p}=1.96\times0.009=0.01764\approx0.018[/tex]
Thus, the margin of error is 0.018.
(c)
The (1 - α) % confidence interval for population proportion is:
[tex]CI=\hat p\pm MOE[/tex]
Compute the 95% confidence interval for population proportion as follows:
[tex]CI=\hat p\pm MOE\\=0.28\pm 0.018\\=(0.262, 0.298)[/tex]
Thus, the 95% confidence interval for population proportion is (0.262, 0.298).
From the information given regarding the statistics, the best point estimate will be 0.28.
How to calculate the point estimate
From the given information, the best point estimate will be:
p = x/n
= 735/2625
= 0.28
Also, the margin of error will be:
1960 × ✓0.28(1 - 0.28) / ✓2625
= 0.018
Lastly, the 95% confidence interval will be 0.262 < p < 0.298.
Learn more about statistics on:
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