Question

A shoe company takes a random sample of 400 customers who visited their website last month and found that 275 of them actually purchased shoes. Determine the lower limit of a 95% confidence interval (z = 1.96) for the proportion of those people that will purchase shoes if they visit the website. Round the answer to 4 decimal places.

Answer 1

0.6420758

Explanation:

x = 275 ; n = 400

Phat = x / n = 275 / 400 = 0.6875

Z at 95% = 1.96

Confidence interval = phat ± margin of error

Margin of Error :

Z * √phat(1 - phat) / n

1.96 * √0.6875(0.3125) / 400

1.96 * 0.0231756

= 0.0454242

Lower boundary :

Phat - margin of error

0.6875 - 0.0454242

= 0.6420758