π The distribution t is used when the sample size is small (n < 30).

π The t-table is used to determine the critical value based on the significance level and degrees of freedom.

π§ͺ The t-distribution is used to estimate the mean, test hypotheses, and determine the acceptance region.

π The transcript discusses the use of the t-distribution table in statistical analysis.

π The video explains how to calculate the t-value using the formula t = (xΜ - ΞΌ) / (s / βn).

π A specific example is given, where the average time for students to fill out a form is 50 minutes with a standard deviation.

β±οΈ On average, it takes 42 minutes for 12 students to fill out the KRS form, with a standard deviation of 11.9 minutes.

π» The hypothesis is that using a computer can speed up the KRS filling process.

π The significance level is set at 5%, indicating that if the filling time is faster than 50 minutes, the hypothesis is supported.

The video discusses the distribution of t with n less than 30.

The hypothesis is that the mean population is less than 50 minutes.

Using the provided formulas, the calculated value is -2.303.

π The t-distribution is symmetric and has two tails.

βοΈ The t-table is located on the left side of zero.

β Values in the rejection region of the t-table are greater than a certain value.

π When the value of t is less than 30, the critical region for h0 lies on the left side.

π If the calculated t-value falls within the critical region, h0 is rejected.

π If the calculated t-value is greater than the specified t-table value, h0 is accepted.

β The acceptance region signifies that h0 is accepted.

β The rejection region indicates that h0 is rejected.

π In the given context, if h0 is accepted, it means that the conclusion is valid.

π‘ If the calculated t-value falls within the critical region, it suggests that the conclusion is invalid.

β οΈ The t-value being less than 50 minutes implies a left-tailed distribution.

π The t-test value is negative 1.7, which falls in the rejection region of the null hypothesis.

β Therefore, the null hypothesis is rejected and the alternative hypothesis is accepted.

βοΈ The t-test value is smaller than the critical value, indicating that the new computer system is significantly faster than the old system.