Question

2. To test the claim that greater than of size 300 i confidence level (use p-value inethod) n that greater than 2796 of the Americans favor death penalty. a sample an out of which ISO favor death penalty Test the claim at 016 3. A company pays an average of Sil per hour assuming that the sample is taken from a normal population, a sample of 14 workers shows mean wage of $10.5 and sample variance as 50.56. Test the claim that population variance is greater than 0.49. Use cither critical value or p-value method at a = 5%.

Answer 1

Answer:

2)

n=500, x= 150, C= 90%, $\alpha$ = 0.10, P=0.27

150 500 = 0.30

a)

Ho: P$\leq$ 0.27

H1: P > 0.27

b)

Calculate test statistics

P-p p*(1-P)

0.30 – 0.27 0.27+(1-0.27) 500

z = 1.510994713

test statistics = 1.51

Calculate P-Value

P-Value = 1 - P(z < 1.51)

find P(z < 1.51) using normal z table

P(z < 0.1.2659) =0.9345

P-Value = 1 - 0.9345

P-Value = 0.0655

since (P-Value = 0.0655) <  (  $\alpha$ = 0.10)

null hypothesis (Ho) is rejected.

3)

$\mu$= 11, n=14, $\bar x$ =10.5, S²= 0.56, $\sigma ^{2}$ = 0.49

  $\alpha$ =5% = 0.05

Ho: $\sigma ^{2}$ $\leq$  0.49

H1: $\sigma ^{2}$ >  0.49

**(I – u) = 28

X2 – (14 – 1) *0.56 0.49

14.857

Test statistics= 14.857

Calculate Critical value using X² table with

df = n-1 = 14-1 = 13 and $\alpha$ = 0.05

We get critical value as

X² Critical value ​=22.362

Since (Test statistics= 14.857) < (X² Critical value ​=22.362)

it is concluded that the null hypothesis is not rejected.