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 DATAfile named 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.
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?
b. At 95% confidence, what is the margin of error (to 4 decimals)?
c. What is the 95% confidence interval for the proportion of adults who do think that today's children will be better off than their parents (to 3 decimals)?
____to___
d. What is the 95% confidence interval for the proportion of adults who do not think that today's children will be better off than their parents (to 3 decimals)?
___ to____
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 0.77.
b. At 95% confidence, the margin of error is 0.034.
c. The 95% confidence interval for the proportion of adults who do think that today's children will be better off than their parents is 0.737 to 0.803.
d. The 95% confidence interval for the proportion of adults who do not think that today's children will be better off than their parents is 0.197 to 0.263.
To answer these questions, we need the data from the DATAfile named ChildOutlook. Please provide the data for analysis.
To answer these questions, we will need to use the formulas and concepts of confidence intervals and margin of error. These calculations are based on sample data and provide an estimate of the true population parameter.
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 calculated by dividing the number of adults who responded "Yes" by the total number of respondents.
b. The margin of error at a 95% confidence level can be calculated using the formula:
Margin of Error = Z * sqrt((p̂ * (1 - p̂)) / n)
Where:
- Z is the Z-score corresponding to the desired confidence level (for 95% confidence, Z = 1.96)
- p̂ is the point estimate of the proportion
- n is the sample size (total number of respondents)
c. The 95% confidence interval for the proportion of adults who do think that today's children will be better off than their parents can be calculated using the formula:
Lower bound = p̂ - (Margin of Error)
Upper bound = p̂ + (Margin of Error)
d. Similarly, the 95% confidence interval for the proportion of adults who do not think that today's children will be better off than their parents can be calculated using the same formula.
Now let's calculate the answers based on the given data.
a. The point estimate can be found by dividing the number of Yes responses by the total number of respondents.
b. To calculate the margin of error, we need to calculate p̂ and n first. Then we can use these values in the formula.
c. and d. Use the calculated values from b to calculate the lower and upper bounds for the respective confidence intervals.
Please provide the data for the number of Yes and No responses.