Question

g In the sample of 134 South Korean tourists, 57 of them were satisfied with their Jeju experience. In the sample of 150 other country tourists, 72 were satisfied with their Jeju experience. The marketing firm wants to determine if the satisfaction rating of South Korean tourists is less than the satisfaction rating of other country tourists. Notation: 1=South Korean tourists and 2=other country tourists A normal distribution is used to carry out a hypothesis test for this scenario. What is the test statistic for this hypothesis test?

Answer 1

The test statistic = -0.93

Explanation:

The test statistic is given by the formula

z = (X₁ - X₂) ÷ √(σₓ₁² + σₓ₂²)

where X₁ = proportion of data of South Korean tourists = (57/134) = 0.425

X₂ = proportion of other country tourists = (72/150) = 0.48

σₓ₁ = standard error in data 1 = √[p(1-p)/n]

= √(0.425 × 0.575/134) = 0.0427

σₓ₂ = standard error in data 2 = √[p(1-p)/n]

= √(0.48 × 0.52/150) = 0.0408

z = (X₁ - X₂) ÷ √(σₓ₁² + σₓ₂²)

z = (0.425 - 0.48) ÷ √(0.0427² + 0.0408²)

z = -0.055 ÷ 0.0590586996

z = -0.9313

Hope this Helps!!!