a . T e s t s t a t i s t i c : z = 0.37 − 0.20 0.2 ∗ ( 1 − 0.2 ) 100 = 4.25. C r i t i c a l z − v a l u e : z c = 1.96. S i n c e t e s t s t a t i s t i c i s g r e a t e r t h a n t h e c r i t i c a l v a l u e , w e s h o u l d c o n c l u d e t h a t t h e r e i s e n o u g h e v i d e n c e t o r e j e c t t h e c l a i m . b . P − v a l u e f o r z = 4.25 : p < 0.0001. S i n c e P − v a l u e i s l e s s t h a n 0.05 , w e s h o u l d c o n c l u d e t h a t t h e r e i s e n o u g h e v i d e n c e t o r e j e c t t h e c l a i m . c . 95 C I = ( 0.37 − 1.96 0.2 ( 1 − 0.2 ) 100 , 0.37 + 1.96 0.2 ( 1 − 0.2 ) 100 ) = ( 0.29 , 0.45 ) . S i n c e 0.2 d o e s n o t l i e t h a n i n t h e c o n f i d e n c e i n t e r v a l , w e s h o u l d c o n c l u d e t h a t t h e r e i s e n o u g h e v i d e n c e t o r e j e c t t h e c l a i m . a.\;\;Test\;statistic:\;z=\frac{0.37-0.20}{\sqrt{\frac{0.2*(1-0.2)}{100}}}=4.25.\\
Critical\;z-value:\;z_c=1.96.\\
Since\;test\;statistic\;is\;greater\;than\;the\;critical\;value,\;we\;should\;conclude\;that\;\\there\;is\;enough\;evidence\;to\;reject\;the\;claim.\\
b.\;\;P-value\;for\;z=4.25:\;p<0.0001.\\
Since\;P-value\;is\;less\;than\;0.05,\;we\;should\;conclude\;that\;\\there\;is\;enough\;evidence\;to\;reject\;the\;claim.\\
c.\;\;95CI=(0.37-1.96\sqrt{\frac{0.2(1-0.2)}{100}},\;0.37+1.96\sqrt{\frac{0.2(1-0.2)}{100}})=(0.29,\;0.45).\\
Since\;0.2\;does\;not\;lie\;than\;in\;the\;confidence\;interval,\;we\;should\;conclude\;that\;\\there\;is\;enough\;evidence\;to\;reject\;the\;claim.\\ a . T es t s t a t i s t i c : z = 100 0.2 ∗ ( 1 − 0.2 ) 0.37 − 0.20 = 4.25. C r i t i c a l z − v a l u e : z c = 1.96. S in ce t es t s t a t i s t i c i s g re a t er t han t h e cr i t i c a l v a l u e , w e s h o u l d co n c l u d e t ha t t h ere i s e n o ug h e v i d e n ce t o re j ec t t h e c l aim . b . P − v a l u e f or z = 4.25 : p < 0.0001. S in ce P − v a l u e i s l ess t han 0.05 , w e s h o u l d co n c l u d e t ha t t h ere i s e n o ug h e v i d e n ce t o re j ec t t h e c l aim . c . 95 C I = ( 0.37 − 1.96 100 0.2 ( 1 − 0.2 ) , 0.37 + 1.96 100 0.2 ( 1 − 0.2 ) ) = ( 0.29 , 0.45 ) . S in ce 0.2 d oes n o t l i e t han in t h e co n f i d e n ce in t er v a l , w e s h o u l d co n c l u d e t ha t t h ere i s e n o ug h e v i d e n ce t o re j ec t t h e c l aim .
Comments
Leave a comment