In a survey of 5100 TV viewers, 40% said they watch network news programs. Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of TV viewers who watch network news programs. Hint, find the CI using 1-PropZInt, then add and subtract from the proportion to find the margin of error.
Here is one way you can find the margin of error since the problem is using proportions:
Margin of error = (z-value)(√pq/n)
Note: q = 1 - p
Using your data:
Margin of error = (1.96)[√(.40)(.60)/5100)]
Finish the calculation.
288.24
To find the margin of error for this survey, we need to follow these steps:
Step 1: Calculate the sample proportion.
The sample proportion, denoted by p-hat (p̂), is given as 40% or 0.40.
Step 2: Calculate the critical value.
Since we want 95% confidence in our estimate, we need to find the critical value corresponding to the confidence level. For a 95% confidence level, the critical value is approximately 1.96.
Step 3: Calculate the standard error.
The formula for the standard error, denoted by SE, is given as:
SE = √[(p̂ * (1 - p̂)) / n]
Where n is the sample size, which is 5100 in this case.
SE = √[(0.40 * (1 - 0.40)) / 5100]
Step 4: Calculate the margin of error.
The margin of error, denoted by E, is obtained by multiplying the critical value by the standard error:
E = Critical Value * SE
E = 1.96 * √[(0.40 * (1 - 0.40)) / 5100]
Calculating the above expression will give you the margin of error for this survey.
To find the margin of error for this survey, we need to calculate the confidence interval (CI) using the 1-PropZInt function.
Step 1: Find the sample proportion:
In this case, 40% of the 5100 TV viewers said they watch network news programs. So, the sample proportion is 0.40.
Step 2: Calculate the standard error:
The standard error (SE) is the measure of the variability of estimated proportions. It can be calculated using the formula:
SE = √ ((p * q) / n)
Where:
p = sample proportion (0.40 in our case)
q = 1 - p (0.60 in our case)
n = sample size (5100 in our case)
SE = √ ((0.40 * 0.60) / 5100)
Step 3: Determine the critical value:
To achieve 95% confidence in the estimate, we need to find the critical value. For a normal distribution, the critical value is approximately 1.96.
Step 4: Calculate the margin of error:
The margin of error is the range within which the true percentage is likely to fall. It can be calculated by multiplying the critical value with the standard error:
Margin of error = critical value * standard error
Margin of error = 1.96 * √ ((0.40 * 0.60) / 5100)
Calculating this expression will provide the margin of error.