Is this correct? 1. Suppose Y has a 2 distribution with 25 degrees of freedom. U

ID: 3340451 • Letter: I

Question

Is this correct?

1. Suppose Y has a 2 distribution with 25 degrees of freedom. Use R and your calculator to calculate:

(a) P(Y > 55.62)

x2cdf(55.62,1099,24)=2.581x10-4

> pchisq(55.62,24,lower.tail = F) [1] 0.000258097

(b) P(Y > 31.1)

x2cdf(55.62,1099,24)=0.1509202048

> pchisq(31.1,24,lower.tail = F) [1] 0.1509202

x2cdf(10-99,14.01,24)=0.0535758017

> pchisq(14.01,24) [1] 0.0535758

(d) P(Y < 10.88)

x2cdf(10-99,10.88,24)=0.0101577017

> pchisq(10.88,24) [1] 0.0101577

(e) P(8.8 < Y < 19.5)

x2cdf(55.62,1099,24) - x2cdf(10-99,8.8,24)=0.0101577017

> pchisq(8.8,24,lower.tail = F) - pchisq(19.5,24) [1] 0.7228179

Ans:

Part e is wrong.

Verified using Excel function:

(a) P(Y > 55.62)

CHIDIST(55.62,24)=0.000258

(b) P(Y > 31.1)

CHIDIST(31.1,24)=0.15092

1-CHIDIST(14.01,24)=0.05357

(d) P(Y < 10.88)

1-CHIDIST(10.88,24)=0.010158

(e) P(8.8 < Y < 19.5)=P(Y<19.5)-P(Y<8.8)

(1-CHIDIST(19.5,24))-(1-CHIDIST(8.8,24)=CHIDIST(8.8,24)-CHIDIST(19.5,24)=0.9980-0.7248=0.2732

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