Homework 11 Solution : STAT 400 - Spring 20-

Ha Khanh Nguyen

① X = weight of a"

22 - ounce"

Charlie Mulligan 's porterhouse steak .X - N ( µ , 62)

Note : I = 21.4,s'-

- O.64

,n = 6

(a) to : µ= 22

I - Ho 21.4 - 22Teststatisic: T = - =

g= -1.8370

( 6 is unknown) HT

(b) Ho : µ= 22 vs. Hi : µ 522 ( left - sided test )

Tnt* 0.1 df=5 Rejection : Reject to tf TL - to . I , df=5

⇐Ts-i.-

Decision Since 1- ⇐ - 1.837C - 1.476,- taHo at 2=0.1

.

(c) p- value = I ( Tf - 1.837 ) ⇒ O.05cp-valuelo.IT

Tutdf -- 5 Decision Since p- value > x -

- 0.05,

p- value,µ fonjectH at a -- 0.05 .

OR use R,

- 1.837

ptc - 1.837, df - 5)[ I ] 0.06281569 ← p

- value

①

(d) Ho : 6 ¥0.5

Teststatisic : x? =ln÷ = 16-47%642 =

( e) to : G f 0.5 us . Hi 70.5

Idf . 5 Rejection : Reject It ① if X'

> XIdf - 5↳ ⇒xes¥"

Decision since XE 12.8 > 1.610,XLt at a = O

. I.

(f) Suppose 6=0.5. The decision in part (e) is incorrect Type I error,reject to when to is true ( false positives ) was made .

② n = 120. To = 47

120

(a) Ho : p f 0.3 vs . It, :p > 0.3- 47p - Po Tao

- O.3

Teststatistic : Z = -_- =

#= 2.19130

✓ Po(l-p# ✓ 0.3 (0.7)n

( b)p-value = I ( Z 32.1913)

Z - N (O, I )= I - I ( Z C 2.1913)✓¥§

,

p- value

= I - 0.9857 = 0.01430=

2.1913 Decision Since p- value = 0.014342=-0.05,

Ho at a -- 0.05

.

②

(c) Suppose p= 0.25. The decision in (b) wasi Type 1 error

,

rejecting to when Ho is true , was made .

(d) Assuming to is true.

That is,

X = # of students who support universal credit / no- credit,X n Binom ( n = 120

, p= Or32, assuming to is true

in Rp-value = I C X S, 47 ) = P - I ( X f 4G ) I

= I - pbinom ( q = 46 , size-- 120

, prob -- O. 3)

= 0.01997150

③