A random sample of n₁ = 16 communities in western Kansas gave the following information for people under 25 years of age

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A Random Sample Of N 16 Communities In Western Kansas Gave The Following Information For People Under 25 Years Of Age 1 (51.45 KiB) Viewed 13 times

A random sample of n₁ = 16 communities in western Kansas gave the following information for people under 25 years of age. X₁: Rate of hay fever per 1000 population for people under 25 91 122 127 94 123 112 93 96 125 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 94 109 100 97 110 88 110 79 115 100 89 114 85 96 USE SALT (i) Use a calculator to calculate x₁, S₁, X2, and S. (Round your answers to four decimal places.) x₁ = $1 = x₂ = $₂ = (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 a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: M₁ = M₂; H₁: My > H₂ O Ho: M₁ M₂i H₁: M₁ = M₂ O Ho: M₁ = H₂i H₁: M₁ #M₂ O Ho: M₁ = H₂i H₁: M₁ <H₂ (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O 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 μ₁-₂. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. t 0 t P-value P-value t t t P-value P-value
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. O Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50. O Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50. O Fail to reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50. O Fail to reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.