## Question

###### (b) and (c) are what i need help with Problem(7) Let z Student's t-distribution. The density...

(b) and (c) are what i need help with

Problem(7) Let z Student's t-distribution. The density function of T is Normal(0, 1) and Y ~ xã, then the new r.v. T = Jun has the r[(y + 1)/2) -(4+1)/2 fr(t) = + (7/2) (a) (3 points) Describe the similarity/difference between T and Z. (b) (6 points) Let to be a particular value of t. Use t-distribution table to find to values such that the following statements are true. (Given that df=10.) (i) P(-to <t<to) = 0.90. (ii) Pt S-to or t > to) = 0.05. (iii) P(t <to) = 0.025. (c) (4 points) The following random sample was selected from a normal distribution: 11 11 4,6,3,5,9, 3, 4, 4,7,8,5. Hint: &: = 58; x = 346 (i) Construct a 90% confidence interval for the population H. (ii) Construct a 95% confidence interval for the population p.

## Answers

(b) The t-table I will use has computes the probabilities .

(i)

using symmetry of t curve

As it is given that

From the table we get

(ii) using symmetry of t curve we have

As

(iii) Here

c) The sample mean and sample standard deviation is

(i) The confidence interval is given by

Use b) (i) part

(ii) Here the interval is

We were unable to transcribe this imageWe were unable to transcribe this imageP(-to <t<to) = 0.90 →1-2P(t <-to) = 0.90 P(t <-to) = 0.05We were unable to transcribe this imageP(t <-to or t > to) = 2P(t <-to)We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

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