a random sample of 75 juniors are asked whether they plan to attend homecoming. of these, 62 juniors said they will attend. what is the margin of error at 90% confidence and its interpretation? 0.072; 90% of the time we will capture the true proportion of juniors who will attend homecoming within 0.072 of the population proportion 0.072; we are 90% confident that the true proportion of juniors who will attend homecoming is within 0.072 of the sample proportion 0.086; we are 90% confident that the true proportion of juniors who will attend homecoming is within 0.086 of the sample proportion 0.086; 90% of the time we will capture the true proportion of juniors who will attend homecoming within 0.086 of the population proportion

The margin of error, in statistics, is the degree of error in results received from random sampling surveys. A higher margin of error in statistics indicates less likelihood of relying on the results of a survey or poll, i.e. the confidence in the results will be lower to represent a population.

The margin of error at 90% confidence for a random sample of 75 juniors asked whether they plan to attend homecoming, where 62 said they will attend, is approximately 0.086. This means that we are 90% confident that the true proportion of juniors who will attend homecoming is within 0.086 of the sample proportion.

To interpret this, you can say that "we are 90% confident that the true proportion of juniors who will attend homecoming is within 0.086 of the sample proportion." This means that if you were to repeat the sampling process multiple times, the true proportion of juniors who will attend homecoming would fall within the margin of error around the sample proportion 90% of the time.

The margin of error is a measure of the precision of a sample estimate. It is calculated by multiplying the standard error of the sample proportion by a constant called the critical value. The critical value depends on the level of confidence you want to have in your estimate. In this case, the critical value for a 90% confidence level is approximately 1.645.

The standard error of the sample proportion is calculated using the following formula:

Standard error = √((sample proportion * (1 - sample proportion)) / sample size)

Plugging in the values for the sample proportion (62/75) and sample size (75), you get a standard error of approximately 0.072.

Multiplying the standard error by the critical value gives the margin of error:

The margin of error = critical value * standard error

= 1.645 * 0.072

= 0.086

Hence, the margin of error at a 90% confidence level for this sample is approximately 0.086.

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