A sample of 200 students in a English class were asked- How long did you sleep last night?
sample mean: 6.4 hours
S.D. = 1.6 HOURS
Standard Error = .11 hours
sample size = 200
What type of data is used in this example?
my answer: MEASUREMENT DATA
What would happen to the size of the Margin of error or confidence interval if the level of confidence were instead 68% and why?
My answer: the Margin of error would decrease because the level of confidence increased????
You used measures of central tendency and variability.
What was it before it was 68%? If the confidence interval increased, then your answer would be right.
In this example, the data used is indeed measurement data. This is because the question asked the students to provide a numerical value (number of hours slept) rather than choosing from a pre-defined set of options.
Now, let's discuss how changing the level of confidence would affect the size of the margin of error or confidence interval. First, let's understand what these terms mean.
The margin of error is a measure of the uncertainty or variation in an estimate based on a sample. It represents the range within which the true population parameter is likely to lie. It is determined by factors such as the sample size, standard deviation, and level of confidence.
The level of confidence represents the probability or likelihood that the interval estimate (confidence interval) contains the true population parameter. It is usually expressed as a percentage, such as 90%, 95%, or 99%.
In general, as the level of confidence increases, the margin of error or confidence interval will also increase. This is because a higher level of confidence requires a wider interval to accommodate more possible values of the true population parameter.
Conversely, if the level of confidence is reduced, the margin of error or confidence interval will decrease. This is because a narrower interval is needed to achieve a lower level of confidence.
So, to provide the correct answer to your question, if the level of confidence were instead 68%, the margin of error or confidence interval would decrease because a narrower range would be required to achieve the lower level of confidence.