Final answer:
Using a sample proportion of 0.30 and a standard error of 0.0458 with a 99% confidence level, the 99% confidence interval for the true proportion of songs by male artists on Jacob's phone is between 18.2% and 41.8%. Several factors such as sampling bias and non-response bias can affect the survey's outcome beyond just the margin of error.
Step-by-step explanation:
To create a 99% confidence interval for the proportion of songs on Jacob's phone that are by a male artist, we can use the sample proportion and the standard error for the proportion. In the sample of 100 songs, 30 are by male artists, so the sample proportion (π) is 0.30.
The formula to calculate the confidence interval is:
Confidence Interval = π ± (z* × SE)
where SE is the standard error of the sample proportion and z* is the z-value that corresponds to the desired confidence level.
The standard error (SE) is calculated by the formula:
SE = √((π(1 - π)) / n)
Since the confidence level is 99%, the z-value (z*) is 2.576 (which you can find in a standard Z-table).
Let's calculate the SE:
SE = √((0.30(1 - 0.30)) / 100)
SE = 0.0458
Now, we can calculate the 99% confidence interval:
Confidence Interval = 0.30 ± (2.576 × 0.0458)
Confidence Interval = 0.30 ± 0.1180
Therefore, the 99% confidence interval for the true proportion of songs by male artists on Jacob's phone is approximately 18.2% to 41.8%.
Factors Affecting the Survey's Outcome:
There may be several factors affecting the survey's outcome that are not covered by the margin of error, including:
- Sampling bias if the SRS is not properly randomized
- Non-response bias if certain individuals are less likely to be sampled
- Measurement error if there's a mistake in how the data are collected or recorded