Question

Question 4 (of 5) 10.00 points Find the sample proportions and test statistic for equal proportions (a-1) Dissatisfied workers in two companies 저 Ⅱ 38, n1 100, x2 :28, n2 : 100, a = 05, two-tailed test Round your answers to 4 decimal places. Use Excel to calculate the p-value.) pt P2 p value 702 (a-2) Choose the appropriate hypotheses a 3) Based on the dala soject Ho True False 0-14-4xs AStat 1 Exam 1 Re.docx 4 Stat il Exam 1 Re..docx Type here to search 46 3 4 5 6 7 8 9

Answer 1

Part a)

Given,

x₁ = 38

n₁ = 100

x₂ = 28

n₂ = 100

alpha = 0.05

a1)

p₁ = 38/100 = 0.38

p₂ = 28/100 = 0.28

p_c = (n₁p₁ + n₂p₂)/(n₁+n₂) = 0.33

Z_Calc = (p1-p2)/sqrt(p_c * (1-p_c)/n₁ + p_c * (1-p_c)/n₂) = 1.5038

p-value = .132633

Z_alpha/2 = +/-1.96

a2)

Option a

a3)

Option b ie False

Part b)

Given,

x₁ = 22

n₁ = 200

x₂ = 10

n₂ = 50

alpha = 0.01

b1)

p₁ = 22/200 = 0.11

p₂ = 10/50 = 0.2

p_c = (n₁p₁ + n₂p₂)/(n₁+n₂) = 0.128

Z_Calc = (p1-p2)/sqrt(p_c * (1-p_c)/n₁ + p_c * (1-p_c)/n₂) = -1.7038

p-value = .044284

Z_alpha = -2.326

b2)

Option b

b3)

Option b ie False

Part c)

Given,

x₁ = 34

n₁ = 480

x₂ = 24

n₂ = 520

alpha = 0.05

c1)

p₁ = 34/480 = 0.0708

p₂ = 24/520 = 0.0462

p_c = (n₁p₁ + n₂p₂)/(n₁+n₂) = 0.058

Z_Calc = (p1-p2)/sqrt(p_c * (1-p_c)/n₁ + p_c * (1-p_c)/n₂) = 1.6681

p-value = .047648

Z_alpha = 1.96