Math Problem Statement

A company would like to know if efficiency can be improved through a training course for employees. A sample of employees is taken. The time taken for an employee to complete a task before training and after training is observed.

Solution

It seems like you've uploaded an image with data related to a hypothesis test for comparing the time it takes employees to complete tasks before and after training. Based on the provided information, we have a few statistical details to work with.

Here’s a breakdown of the key information:

  • Mean Before Training: 33.1
  • Mean After Training: 31.7
  • Variance Before Training: 16.81
  • Variance After Training: 12.25
  • Number of Observations (n): 30
  • Degrees of Freedom (df): 29
  • t Statistic: -2.282
  • p-value (one-tail): 0.051
  • t Critical Value (two-tail): ±1.699
  • Confidence Level: 95%

We also need to calculate the point estimate for after training and complete some other missing values. I can help with that.

Let me walk you through some of the steps:

  • Degrees of freedom (df): For a paired sample t-test, degrees of freedom can be calculated as n1n - 1. Given that n=30n = 30, the degrees of freedom would be 301=2930 - 1 = 29, which is already provided.

  • Point estimate for after training: It seems that the point estimate for before training is given as 1.234 (which is the average difference between before and after training in terms of the task completion time).

Would you like me to calculate the final value for the point estimate after training?

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing
Paired Sample t-Test
Confidence Intervals

Formulas

t = (x̄_before - x̄_after) / (s / √n)
Degrees of Freedom = n - 1

Theorems

t-distribution
Paired t-test

Suitable Grade Level

Grades 11-12