Question

If 34 out of 50 planted seeds sprout within a week, find a 95% confidence interval for the proportion of all seeds that will sprout within a week.

a. 0.499 to 0.778
b. 0.488 to 0.789
c. 0.511 to 0.766
d. 0.522 to 0.755

Answer 1

To find the 95% confidence interval for the proportion of all seeds that will sprout within a week, use the formula CI = p ± z * √((p(1-p))/n). Plugging in the values, the confidence interval is approximately 0.5801 to 0.7799.

Step-by-step explanation:

To calculate the 95% confidence interval for the proportion of all seeds that will sprout within a week, we can use the formula:

CI = p ± z * √((p(1-p))/n)

Where:

• p = proportion of sprouted seeds (34/50 = 0.68)
• z = z-score for a 95% confidence level (from Z-table, approximately 1.96)
• n = sample size (50)

Plugging in the values, we get:

CI = 0.68 ± 1.96 * √((0.68 * (1-0.68))/50)

CI ≈ 0.68 ± 0.0999

Therefore, the 95% confidence interval for the proportion of all seeds that will sprout within a week is approximately 0.5801 to 0.7799. So, the answer is Option a. 0.499 to 0.778.