Question

A statistician selects a random sample of 200 seeds from a large shipment of a certain variety of tomato seeds and tests the sample for percentage germination. If 155 of the 200 seeds germinate, then a 95% confidence interval for p, the population proportion of seeds that germinate is:

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 155 / 200 = 0.775

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.775 * 0.225) / 200)

= 0..058

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.775 - 0.058 < p < 0.775 + 0.058  

0.717 < p < 0.833

A 95% confidence interval for p, the population proportion of seeds that germinate is: (0.717 , 0.833)