Question

In: Statistics and Probability

Grace is sampling the family harvest of tomatoes. She randomly selects 359 tomatoes and inspects them...

Grace is sampling the family harvest of tomatoes. She randomly selects 359 tomatoes and inspects them for cracking. Of the 359 tomatoes sampled, 119 of them were cracked. Construct a 99% Confidence interval of the proportion of tomatoes suffering from cracks. Answer with the upper bound only. Round to 4 decimal places, as needed.

Solutions

Expert Solution

Solution :

Given that,

n = 359

x = 119

Point estimate = sample proportion = = x / n = 119/359=0.331

1 -   = 1- 0.331 =0.669

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.331*0.669) / 359)

= 0.0640

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.331-0.0640 < p < 0.331+ 0.0640

0.2670< p < 0.3950

The 99% confidence interval for the population proportion p is : 0.2670, 0.3950


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