Question

The mean yearly income (converted in CAD) for a sample of 146 people in the Isle of Balar is $50318.02. From comparable case studies the population standard deviation can be assumeo to be $3193.57. Construct a 95% confidence interval for the mean yearly income of the whole population in the Isle of Balar (round the limits to the unit) Lower limit = Upper limit =

Answer 1

To construct a 95% confidence interval for the mean yearly income of the whole population, use the formula lower limit = sample mean - (Z * (sample standard deviation / sqrt(sample size)) and upper limit = sample mean + (Z * (sample standard deviation / sqrt(sample size))), where Z is the Z-score for a 95% confidence level.

Step-by-step explanation:

To construct a 95% confidence interval for the mean yearly income of the whole population in the Isle of Balar, we can use the formula:

Lower Limit = Sample Mean - (Z * (Sample Standard Deviation / sqrt(Sample Size)))

Upper Limit = Sample Mean + (Z * (Sample Standard Deviation / sqrt(Sample Size)))

Where:

• Sample Mean is the mean yearly income of the sample (50318.02)
• Z is the Z-score for a 95% confidence level (which is 1.96)
• Sample Standard Deviation is the standard deviation of the sample (3193.57)
• Sample Size is the number of people in the sample (146)

Using these values, we can calculate:

Lower Limit = 50318.02 - (1.96 * (3193.57 / sqrt(146))) = 49490.56

Upper Limit = 50318.02 + (1.96 * (3193.57 / sqrt(146))) = 51145.48

Therefore, the 95% confidence interval for the mean yearly income of the whole population in the Isle of Balar is $49491 to $51145.