Respuesta :
Answer:
The margin of error is the range of values below and above the sample statistic in a confidence interval.
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error is given by:
[tex] ME = z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}} =0.04[/tex]
So then the confidence interval is given by:
[tex] Lower =0.14-0.04=0.10[/tex]
[tex] Upper = 0.14+0.04=0.18[/tex]
So then the confidence interval would be given by (0.10,0.18)
The confidence level is not given but we can assume it as [tex]1-\alpha[/tex], and we can conclude at [tex](1-\alpha)*100 \%[/tex] that the true population proportion of people who prefer chocolate is between 0.10 and 0.18
Step-by-step explanation:
Data given and notation
n=1000 represent the random sample taken
[tex]\hat p=0.14[/tex] estimated proportion of interest
[tex]\alpha[/tex] represent the significance level (no given, but is assumed)
ME= 4% =0.04 represent the margin of error
p= population proportion
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Calculating the interval for the proportion
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error is given by:
[tex] ME = z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}} =0.04[/tex]
So then the confidence interval is given by:
[tex] Lower =0.14-0.04=0.10[/tex]
[tex] Upper = 0.14+0.04=0.18[/tex]
So then the confidence interval would be given by (0.10,0.18)
The confidence level is not given but we can assume it as [tex]1-\alpha[/tex], and we can conclude at [tex](1-\alpha)*100 \%[/tex] that the true population proportion of people who prefer chocolate is between 0.10 and 0.18
