Statistical Inference Quiz

What is the purpose of inferential statistics?

• To make generalizations about a population without using a sample

• To estimate the value of a population proportion using the entire population

• To measure the exact value of a population proportion

• To describe and make inferences about a population using a random sample

What does the margin of error represent in statistical inference?

• The exact value of the population proportion

• The maximum likely difference between the sample proportion and the population proportion

• The range of values within the sample proportion

• The minimum likely difference between the sample proportion and the population proportion

What is the formula for the margin of error?

• E = n

• E = 1 / √n

• E = √n

• E = 1 - √n

What is the confidence interval for a population proportion using the margin of error?

• ˆp−1/√n < p < ˆp+1/√n

• ˆp−2/√n < p < ˆp+2/√n

• ˆp−3/√n < p < ˆp+3/√n

• ˆp−4/√n < p < ˆp+4/√n

What is the formula for the test statistic in hypothesis testing for a population mean?

• z = (x̄ - μ) * (σ / n)

• z = (x̄ - μ) / σ

• z = (x̄ - μ) / (σ / √n)

• z = (x̄ - μ) / n

What does the p-value represent in hypothesis testing?

• The exact value of the test statistic

• The likelihood of the data occurring under the null hypothesis

• The range of values within the confidence interval

• The maximum likely difference between the sample mean and the population mean

What is the critical value for a 5% level of significance in a two-tailed hypothesis test?

• ±2.33

• ±1.64

• ±2.58

• ±1.96

What is the purpose of creating a sampling distribution of the means of multiple samples?

• To calculate the margin of error

• To measure the exact value of a population mean

• To estimate the value of a population proportion

• To find the standard error of the mean

What is the 95% confidence interval for the mean weight of the footballs in the consignment?

• 79.93g < μ < 82.97g

• 81.4g < μ < 86.2g

• 77.5g < μ < 85.3g

• 80.1g < μ < 83.9g

What can be concluded from the p-value of 0.0548 in a two-tailed hypothesis test at the 5% level of significance?

• The result is significant, so the null hypothesis is not rejected

• The result is not significant, so the null hypothesis is rejected

• The result is significant, so the null hypothesis is rejected

• The result is not significant, so the null hypothesis is not rejected