Understanding the Student's t-Distribution

This video tutorial explains how to solve statistical problems using the student's t-distribution table. It covers constructing confidence intervals for a population mean when the sample standard deviation is known and the sample size is less than 30. Two problems are discussed: calculating the confidence interval for the average weight of students and determining the mean and standard deviation of chemistry class scores. The video also demonstrates how to find the t-value using the t-distribution table and calculate the margin of error.

Why is the student's t-distribution used instead of the normal distribution in this problem?

• Because the population standard deviation is known

• Because the sample size is greater than 30

• Because the sample mean is exactly 165

• Because the sample size is less than 30 and the population standard deviation is unknown

What is the degrees of freedom used in the calculation of the t-value?

• 21

• 19

• 20

• 18

What is the calculated t-value for 19 degrees of freedom and an alpha over 2 value of 0.025?

• 2.576

• 2.093

• 1.645

• 1.833

What is the margin of error for the confidence interval of the average weight of students?

• 165

• 4.5

• 9.4185

• 2.106

What is the 95% confidence interval for the average weight of students?

• 150 to 180

• 162.8 to 167.106

• 160 to 170

• 165 to 170

What is the sample mean of the chemistry class scores?

• 69

• 80

• 84

• 76

What is the formula used to calculate the sample standard deviation?

• s = sqrt((sum of x - x̄)^2 / n)

• s = (sum of x - x̄) / (n-1)

• s = sqrt((sum of x - x̄)^2 / (n-1))

• s = (sum of x - x̄) / n

What is the calculated sample standard deviation for the chemistry class scores?

• 12.3

• 11.709

• 9.8

• 10.5

What is the t-value used for the chemistry class problem with 9 degrees of freedom and an alpha over 2 value of 0.05?

• 2.576

• 2.093

• 1.8331

• 1.645

What is the 90% confidence interval for the mean score of the chemistry class?

• 70 to 90

• 73.213 to 86.787

• 75 to 85

• 80 to 90