Compare the results to those obtained in part a how does increasing the level of confidence affect the size of the margin of error E?
Increasing the level of confidence will decrease the size of the margin of error E. This is because a higher level of confidence indicates that the sample size is larger and the data is more reliable. As the sample size increases, the margin of error decreases.
To compare the results obtained in part a and examine the impact of increasing the level of confidence on the size of the margin of error (E), you need to understand the relationship between confidence level and margin of error.
In statistics, the margin of error (E) represents the range within which the true population parameter is likely to fall. It is typically expressed as a range, such as plus or minus a certain value. The margin of error is influenced by various factors, including the sample size, standard deviation, and the desired level of confidence.
The level of confidence is a measure of the certainty or probability that the calculated interval contains the true population parameter. It is typically represented as a percentage and is used to determine the width of the confidence interval.
When it comes to the relationship between the level of confidence and the margin of error, it's important to understand that increasing the level of confidence leads to a larger margin of error. This means that as you aim for increased confidence, the range within which the true population parameter is likely to fall becomes wider.
To quantify this relationship mathematically, let's assume that you conducted a survey and calculated a margin of error (E) with a certain level of confidence, denoted as C1. If you were to increase the level of confidence to a higher value, denoted as C2 (C2 > C1), the margin of error would also increase.
The reason for this is that as the level of confidence increases, the critical value for the corresponding confidence interval becomes larger. The critical value is a factor determined by the desired confidence level, sample size, and the distribution of the data. The larger critical value contributes to a wider confidence interval, resulting in a larger margin of error.
To compare the results obtained in part a with different levels of confidence, you would need to examine and compare the values of the margin of error calculated for each confidence level. This will allow you to observe how the margin of error changes as the level of confidence is increased.
To compare the results obtained in part A and understand how increasing the level of confidence affects the size of the margin of error (E), we need to consider the relationship between confidence level and margin of error.
In general, as we increase the level of confidence, the margin of error (E) also increases. This means that a higher level of confidence requires a wider interval and a larger margin of error.
To explain this further, let's recall the formula for calculating the margin of error:
E = Z * (σ/√n)
In this equation, Z represents the Z-score corresponding to the desired level of confidence, σ represents the standard deviation of the population, and n represents the sample size.
When we increase the level of confidence, we use a larger Z-score value. The Z-score represents the number of standard deviations that the desired confidence level corresponds to. By using a larger Z-score, we are capturing a larger proportion of the population in the confidence interval.
Since the margin of error (E) is directly proportional to the Z-score, an increase in the level of confidence (and consequently the Z-score) will result in a larger margin of error.
Therefore, increasing the level of confidence widens the confidence interval and increases the size of the margin of error (E). This is because a higher level of confidence requires more certainty and thus a larger interval to capture the true population parameter with a higher degree of confidence.