To find the 89% confidence interval for the probability of flipping a head with this coin, follow these steps:
1. Calculate the sample proportion (p-hat) by dividing the number of heads (52) by the total number of flips (100):
p-hat = 52/100 = 0.52
2. Determine the standard error (SE) by using the formula:
SE = sqrt(p-hat * (1 - p-hat) / n)
where n is the total number of flips. In this case, n = 100.
SE = sqrt(0.52 * 0.48 / 100) ≈ 0.0499
3. Find the critical value (z) corresponding to the 89% confidence interval. You can use a z-table or an online calculator to find this value. For an 89% confidence interval, the critical value is approximately 1.645.
4. Calculate the margin of error (ME) using the critical value (z) and standard error (SE):
ME = z * SE
ME = 1.645 * 0.0499 ≈ 0.0821
5. Determine the confidence interval by adding and subtracting the margin of error from the sample proportion:
Lower limit = p-hat - ME = 0.52 - 0.0821 ≈ 0.4379
Upper limit = p-hat + ME = 0.52 + 0.0821 ≈ 0.6021
So, the 89% confidence interval for the probability of flipping a head with this coin is approximately 0.4379 to 0.6021.