Concept explainers
To identify: the correct option among options (a) to (d) about statements I, II, III given below.
For a t distribution, with df degrees of freedom,
- It is symmetric.
- It has more variability than a t distribution with df+1 degrees of freedom
- As df increases, the t distribution approaches the standard
Normal distribution .
The options are given by
(a)I only (b)II only (c)III only (d)I and II (e) I,II and III
Answer to Problem 26PT4
Correct option is (e) I, II and III. All statements given above are correct.
Explanation of Solution
- The statement is correct becuase t distribution is symmetric about zero as it’s
- the statement is correct because The variance of t distribution with df degrees of freedom is . Hence variance of t distribution with df+1 degree of freedom is . Let df be equal to x. This means that is to be proved consider,
- This statement is also correct as the curve becomes mesokurtic as degrees of freedom increase and approaches normal distribution.
The probability function of t distribution is a function of the form below which is symmetric about zero
Hence above statement is true that variance of t distribution with df degrees of freedom is more than that with df+1 degree of freedom.
Conclusion: All three statements are correct and correct option is (e)
Chapter 12 Solutions
The Practice of Statistics for AP - 4th Edition
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