Estimating a Population Mean

Find the value of z_c for a 90% confidence interval.

• -1.96 

• 1.645

• 1.440

• -1.598

What is the critical value z_c for a 99% confidence interval?

• 2.33

• 1.96

• 2.58

• 1.645

Answer explanation

The critical value z_c for a 99% confidence interval is 2.58, which corresponds to the z-score for a 99% confidence level in a standard normal distribution.

The margin of error (E) in a confidence interval calculation is determined by which of the following?

• Sample size and standard deviation

• Critical value and standard error

• Sample mean and population mean

• Population proportion and sample proportion

Answer explanation

The margin of error (E) in a confidence interval calculation is determined by the critical value and standard error.

For a 95% confidence interval, what is the z-value used in the calculation?

• 1.96

• 2.33

• 1.645

• 2.58

Answer explanation

The correct z-value for a 95% confidence interval is 1.96, which is used in the calculation of the interval.

Which of the following best describes the purpose of a confidence interval in statistical analysis?

• To estimate the range within which the true population parameter lies with a certain level of confidence

• To calculate the exact value of the population parameter

• To determine if the sample mean is equal to the population mean

• To test the significance of the sample data

Answer explanation

The purpose of a confidence interval is to estimate the range within which the true population parameter lies with a certain level of confidence.

Which of the following is true about the 95% confidence interval for the mean?

• It contains the true population mean 95% of the time

• It is wider than the 99% confidence interval for the same data

• It guarantees that 95% of the sample data falls within the interval

• It remains constant regardless of the sample size

Which of the following values below represents the critical value for a 98% confidence interval?

• 2.326

• 2.054

• 1.645

• 3.091

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

• 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144

• We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. 

• 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144

• We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

Given a population consisting of values (6,3,8,9,4). What is the population mean?

• 5

• 5.5

• 6

• 6.5

The mean score of the random sample of 49 Grade 11 students who took the first periodic test is calculated to be 78. The population variance is known to be 0.16. The confidence level is equal to 95. What is the value of Z_{\frac{\alpha}{2}} ?

• 0.05

• 0.025

• 0.475

• 1.96