Estimating an Average of a Population

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 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

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.

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.

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

• 2.326

• 2.054

• 1.645

• 3.091

The average of the set {–1, 3, 0, –2, 4, 2, x, y} is 3 and (x – y) = 2. What is the value of y?

• 8

• 9

• 10

• 11

Answer explanation

Tags

CCSS.7.EE.B.3

True or False. The t-distribution becomes similar to the standard normal distribution as sample size becomes larger.

• True

• False

Answer explanation

True. As n increases, the t-distribution will approach the standard normal distribution.

Which refers to the method of making decisions about the parameters of a population based on random sampling? It helps to assess the relationship between the dependent and independent variables.

• Inferential statistics

• Data collection

• Descriptive statistics

• Exploratory data analysis

Answer explanation

Statistical inference draws conclusions about a population or process from sample data. It also provides a statement of how much confidence we can place in our conclusions (Moore, et.al, 2017).

Which area of statistical inference refers to the process of estimating the value of a parameter from information obtained from a sample?

• Data analysis

• Estimation

• Test of significance

• Hypothesis Testing

The average salary for a Civil Engineer in the Philippines is Php260,043.00 per year. (PayScale) Which area of statistical inference describes the statement?

• Data analysis

• Test of significance

• Hypothesis testing

• estimation