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(c) in a survey of 1100 work places. it is found that 935 conform to safety regulations
construct an approximate 95% confidence for the true proportion of work places conforming
to safety regulations
To construct an approximate 95% confidence interval for the true proportion of work places conforming to safety regulations, you can use the formula:
Confidence interval = sample proportion ± margin of error
The sample proportion is calculated by dividing the number of work places conforming to safety regulations by the total number of work places surveyed:
Sample proportion = 935 / 1100 = 0.85
The margin of error can be determined using the formula:
Margin of error = critical value * standard error
The critical value can be found by determining the Z-score associated with a 95% confidence level. For a 95% confidence level, the critical value is approximately 1.96.
The standard error can be calculated using the formula:
Standard error = √[(sample proportion * (1 - sample proportion)) / sample size]
Substituting the known values into the formula, we get:
Standard error = √[(0.85 * (1 - 0.85)) / 1100] ≈ 0.0116
Now, we can find the margin of error:
Margin of error = 1.96 * 0.0116 ≈ 0.0228
Finally, we can construct the approximate 95% confidence interval by subtracting and adding the margin of error from the sample proportion:
95% Confidence interval = 0.85 ± 0.0228
Therefore, the approximate 95% confidence interval for the true proportion of work places conforming to safety regulations is approximately 0.8272 to 0.8728.