객관식
Find the following probabilities for a sample size of 75:
(A) ______________
(B) ______________
(C) OR ____________
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7. Sampling Distributions & Confidence Intervals: Mean
Finding Probabilities and T Critical Values - Excel
Multiple Choice
For a sample size of 75, find the following t-scores.
(A) The critical values needed to create a confidence interval.
(B) The t-score with a left probability of .
(C) The t-score with a right tail probability of .
A
(A) (B) (C)
B
(A) (B) (C)
C
(A) (B) (C)
D
(A) (B) (C)
검증된 단계별 안내1
Identify the degrees of freedom (df) for the t-distribution, which is the sample size minus 1: \(df = 75 - 1 = 74\).
For part (A), find the critical t-values for a 90% confidence interval. Since the confidence level is 90%, the total area in the two tails is \(1 - 0.90 = 0.10\). Divide this by 2 to get the area in each tail: \(0.10 / 2 = 0.05\). Use the t-distribution table or software to find the t-score corresponding to a right tail probability of 0.05 with 74 degrees of freedom. The critical values will be symmetric, so the interval is \((-t_{0.05,74}, t_{0.05,74})\).
For part (B), find the t-score with a left-tail probability of 0.087. This means you need the t-value \(t\) such that \(P(T \leq t) = 0.087\) for \(df = 74\). Use the t-distribution table or software to find this value directly.
For part (C), find the t-score with a right-tail probability of 0.025. This means you want the t-value \(t\) such that \(P(T \geq t) = 0.025\) for \(df = 74\). Use the t-distribution table or software to find this value. Note that this t-score will be positive because it corresponds to the upper tail.
Summarize the results: (A) the critical values form a symmetric interval around zero, (B) the t-score corresponds to the 8.7th percentile (left tail), and (C) the t-score corresponds to the 2.5th percentile from the right tail.
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