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

x₁: Rate of hay fever per 1000population for people under 25

100	92	122	129	94	123	112	93
125	95	125	117	97	122	127	88

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

x₂: Rate of hay fever per 1000population for people over 50

94	109	100	95	110	88	110
79	115	100	89	114	85	96

(i) Use a calculator to calculate x₁,s₁, x₂, ands₂. (Round your answers to two decimalplaces.)

x1	=
s1	=
x2	=
s2	=

(ii) Assume that the hay fever rate in each age group has anapproximately normal distribution. Do the data indicate that theage 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 areyou making?

The Student's t. We assume that both populationdistributions are approximately normal with known standarddeviations.The Student's t. We assume that both populationdistributions are approximately normal with unknown standarddeviations.    The standard normal. We assumethat both population distributions are approximately normal withunknown standard deviations.The standard normal. We assume thatboth population distributions are approximately normal with knownstandard deviations.

What is the value of the sample test statistic? (Test thedifference μ₁ − μ₂. Roundyour 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

d) Sketch the sampling distribution and show the area correspondingto the P-value.

(e) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis? Are the data statisticallysignificant at level α?

At the α = 0.05 level, we reject the null hypothesisand conclude the data are not statistically significant.At theα = 0.05 level, we fail to reject the null hypothesis andconclude the data are statisticallysignificant.    At the α = 0.05 level,we reject the null hypothesis and conclude the data arestatistically significant.At the α = 0.05 level, we failto reject the null hypothesis and conclude the data are notstatistically significant.

(f) Interpret your conclusion in the context of theapplication.

Reject the null hypothesis, there is insufficient evidence thatthe mean rate of hay fever is lower for the age group over50.Reject the null hypothesis, there is sufficient evidence thatthe mean rate of hay fever is lower for the age group over50.    Fail to reject the null hypothesis,there is sufficient evidence that the mean rate of hay fever islower for the age group over 50.Fail to reject the null hypothesis,there is insufficient evidence that the mean rate of hay fever islower for the age group over 50.