Answer :
The margin of error on the survey is 0.882 (without the ± sign).
Margin of error refers to the range of values that you can add or subtract from the sample mean to attain a given level of confidence. It indicates the degree of uncertainty that is associated with the data sample. Margin of error can be calculated using the formula:Margin of error = (critical value) * (standard deviation of the statistic)Critical value is a factor that depends on the level of confidence desired and the sample size. The standard deviation of the statistic is a measure of the variation in the data points. Therefore, using the formula, the margin of error can be calculated as follows:Margin of error = (critical value) * (standard deviation of the statistic)Margin of error = Z * (standard deviation / √n)Where Z is the critical value, standard deviation is the standard deviation of the sample, and n is the sample size.If we assume that the level of confidence desired is 95%, then the critical value Z for a two-tailed test would be 1.96. Therefore:Margin of error = Z * (standard deviation / √n)Margin of error = 1.96 * ((172 - 154) / 2) / √nMargin of error = 1.96 * (9 / 2) / √nMargin of error = 8.82 / √nThe margin of error, therefore, depends on the sample size. If we assume a sample size of 100, then:Margin of error = 8.82 / √100Margin of error = 0.882
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