Question

There are 320 welders employed at the Weller Shipyards Corporation. A sample of 45 welders revealed that 36 had graduated from a registered welding course. Construct the 95% confidence interval for the proportion of all welders who graduated from a registered welding course. (Round the final answers to 3 decimal places.)

The confidence interval is between       and     .

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 36 / 45 = 0.800

1 - = 1 - 0.800 = 0.2

Z/2 = 1.96

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

= 1.96 * (((0.800 * 0.2) / 45)

Margin of error = E = 0.117

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.800 - 0.117 < p < 0.800 + 0.117

0.683 < p < 0.917

The confidence interval is between 0.683 and 0.917