MATH 110 Module 7 Exam (Latest-2025) / MATH110 Introduction to Statistics: Portage Learning

5/28/25, 11:25 PM Math 110 - Module 7 Exam




Math 110 - Module 7 Exam
Portage Learning

Question

A mayor claims that the unemployment rate in his city is 4%. Many people think that the
unemployment rate is higher. 95 residents of the city are contacted, and it is found that 8 of
them are unemployed. Can the mayor’s claim be supported at a level of significance of α =
0.02? Test the hypothesis.


Answer:

Step 1: Define the hypotheses
Ho: p = 0.04 (The unemployment rate is 4%)
H1: p > 0.04 (The unemployment rate is greater than 4%) ---> right-tailed test


Step 2: Identify the given data
n = 95 (Sample size)
x = 8 (Number of unemployed individuals)
α = 0.02 (Level of significance)


Step 3: Calculate test statistic and rejection region
Critical z-value for α = 0.02:
1 - α = 0.98 ---> From standard normal distribution table, z = 2.05.


Calculate the mean (u) and standard deviation (σ):
u = np
u = 95 × 0.04 = 3.8


σ = √(np(1-p))
σ = √(3.8 × (1 - 0.04)) = √(3.8 × 0.96) ≈ 1.91


Calculate the z-score:
z = (x - u) / σ
z = (8 - 3.8) / 1.91 ≈ 2.20


Step 4: Decision
Since the calculated z-score (2.20) is greater than the critical z-value (2.05), we rej


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