A contest for free movie tickets had contestants estimate the number of gumballs in a large bowl. In reviewing the results of a random sample of guesses, a contestant regulator found the mean guess was x¯=136 gumballs, with a margin of error of 13 gumballs. Construct a confidence interval for the mean number of guesses.
To construct a confidence interval for the mean number of guesses, we would use the formula:
CI = x¯ ± E
where CI represents the confidence interval, x¯ represents the sample mean, and E represents the margin of error.
Given that x¯ = 136 gumballs and E = 13 gumballs, we can substitute these values into the formula to find the confidence interval.
CI = 136 ± 13
This gives us the confidence interval of (123, 149).
Therefore, we can say with confidence that the mean number of guesses for the number of gumballs in the large bowl falls within the range of 123 to 149 gumballs.
To construct a confidence interval for the mean number of guesses, we need to know the sample mean (x̄) and the margin of error.
Given:
Sample mean (x̄) = 136 gumballs
Margin of error = 13 gumballs
The formula for a confidence interval for the population mean is:
Confidence Interval = x̄ ± Margin of Error
Substituting the given values into the formula, we get:
Confidence Interval = 136 ± 13
Calculating the upper and lower bounds of the confidence interval:
Upper Bound = 136 + 13 = 149 gumballs
Lower Bound = 136 - 13 = 123 gumballs
Therefore, the confidence interval for the mean number of guesses is (123, 149) gumballs.