Identify the letter of the choice that best completes the statement or answers the question. When t is used to estimate the margin of error, it is computed by using the t-distribution. The mean of the sample distribution increases; the difference between the mean of the sample distribution and the mean of the population distribution varies according to the number of degrees of freedom. As the number of degrees of freedom increases, the t-distribution gets closer to the standard normal distribution. The significance level becomes larger as the number of degrees of freedom increases. In order to determine an interval for the mean of a population with an unknown standard deviation, a sample of 87 items is selected. The mean of the sample is determined to be 30. The number of degrees of freedom for reading the value is unknown. The t-value for a 95% two-sided confidence interval estimation with 28 degrees of freedom is 2.048. The z-value for a 97% two-sided confidence interval estimation is 1.88. A 90% confidence interval for the population mean is determined to be 800 to 900. If you calculate another confidence interval at 95%, it will be wider. Type I error is the error of rejecting H when it is false. In hypothesis testing, the hypothesis which is tentatively assumed to be true is called the null hypothesis. For setting the decision rule when the population standard deviation is unknown and it is reasonable to assume the underlying population distribution is normal, we use a t-distribution with n-1 degrees of freedom. A hypothesis test in which you could reject the null hypothesis is a two-tailed test.