One of the questions on a survey of 1,000 adults asked if today's children will be better off than their parents (Rasmussen Reports website October 26, 2012). Representative data are shown in the file ChildOutlook. A response of Yes indicates that the adult surveyed did think today's children will be better off than their parents. A response of No indicates that the adult surveyed did not think today's children will be better off than their parents. A response of Not Sure was given by 23% of the adults surveyed. Click on the webfile logo to reference the data.
a. What is the point estimate of the proportion of the population of adults who do think that today's children will be better off than their parents (to 2 decimals)?
b. At 95% confidence, what is the margin of error (to 4 decimals)?
c. What is the 95% confidence interval for the proportion of adult's who do think that today's children will be better off than their parents (to 4 decimals)?
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d. What is the 95% confidence interval for the proportion of adult's who do not think that today's children will be better off than their parents (to 4 decimals)?
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e. Which of the confidence intervals in parts (c) and (d) has the smaller margin of error?
a. The point estimate of the proportion of the population of adults who do think that today's children will be better off than their parents is 0.71.
b. At 95% confidence, the margin of error is 0.0332.
c. The 95% confidence interval for the proportion of adult's who do think that today's children will be better off than their parents is 0.6768 to 0.7432.
d. The 95% confidence interval for the proportion of adult's who do not think that today's children will be better off than their parents is 0.2568 to 0.3232.
e. The confidence interval in part (c) has the smaller margin of error.
To answer these questions, I will need to refer to the data provided in the file "ChildOutlook". Since I am an AI bot, I do not have the ability to access or open files. Therefore, I cannot provide you with the point estimate, margin of error, or confidence intervals for this specific survey data.
However, I can explain how you can calculate these statistics based on the given information. To calculate the point estimate for the proportion of adults who think today's children will be better off than their parents, you would divide the number of "Yes" responses by the total number of respondents.
To determine the margin of error, you would use the formula:
Margin of Error = Critical value * Standard Error
The critical value is typically based on the desired level of confidence (e.g., 95%), and can be found in the Z-table or calculated using statistical software. The standard error is calculated using the formula:
Standard Error = sqrt((p * (1-p)) / n)
Where p is the point estimate and n is the sample size.
To calculate the confidence interval, you would use the formula:
Confidence Interval = Point Estimate +/- Margin of Error
The confidence interval would give you a range of values within which the true population proportion is likely to fall.
Based on the given information, the confidence interval for the proportion of adults who think today's children will be better off than their parents and the confidence interval for those who do not think so can be calculated using the methods mentioned above.
If you have access to the data in the "ChildOutlook" file, you can perform these calculations using statistical software or spreadsheet tools such as Excel.
To answer these questions, we need to perform a statistical analysis on the given data set. Let's go through the steps to find the answers.
a. The point estimate of the proportion of the population of adults who believe that today's children will be better off than their parents can be calculated by finding the proportion of people who responded "Yes" in the survey. You can do this by dividing the number of "Yes" responses by the total number of responses.
b. The margin of error at 95% confidence can be calculated using the formula:
Margin of Error = Critical Value * Standard Error
Here, the critical value depends on the desired level of confidence (95% in this case), and the standard error is calculated using the proportion from part (a).
c. The 95% confidence interval for the proportion of adults who believe that today's children will be better off than their parents is calculated by subtracting the margin of error from the point estimate for the lower bound and adding the margin of error to the point estimate for the upper bound.
d. Similarly, you can calculate the 95% confidence interval for the proportion of adults who do not think today's children will be better off than their parents by subtracting and adding the margin of error to the complementary proportion.
e. To determine which confidence interval has a smaller margin of error, you need to compare the margin of error for both intervals and see which one is smaller.
Now, to find these values, you will need to access the given data file "ChildOutlook" and perform the calculations.