Question

gave the following information for people under 25 years of age.

x₁: Rate of hay fever per 1000 population for people under 25
100 92 122 126 91 123 112 93
125 95 125 117 97 122 127 88

A random sample of n₂ = 14 regions in western Kansas gave the following information for people over 50 years old.

x₂: Rate of hay fever per 1000 population for people over 50
94 109 99 96 111 88 110 79 115 100 89 114 85 96

(i) Use a calculator to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)x₁= s₁= x₂= s₂=
(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use α = 0.05.
(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ > μ₂H₀: μ₁ = μ₂; H₁: μ₁ < μ₂    H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ > μ₂; H₁: μ₁ = μ₂

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.    The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)

(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250    0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

Answer 1