Question

A random sample of n - 16 communities in western Kansas gave the following information for people under 25 years of age. Xqt Rate of hay fever per 1000 population for people under 25 99 92 122 127 94 123 112 93 125 95 125 112 97 122 127 88 A random sample of 14 regions in western Kansas gave the following Information for people over 50 years old, Xg: Rate of hay fever per 1000 population for people over 50 94 109 102 96 110 110 79 115 100 89 114 8S 96 Use a calculator to calculate X, $1,, and sz. (Round your answers to two decimal places.) 0.05. (1) Assume that the hay fever rate in each age group has an approamately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use a (a) What is the level of significance? State the null and alternate hypotheses Ho - Mi Mi Mi 2 Hoi Ni - M H2 Ho - HH > 2 Ho! H H2 (b) What sampling distribution will you use? What assumptions are you making? The Student'st. We assume that both population distributions are approximately normal with unknown standard devations The standard normal. We assume that both population distributions are aproximately normal with n ow standard deviations The standard normal, we asume that both population distributions are approximately normal with new standard deviation The students. We assume that both population distributions are approximately normal with and deviation What is the value of the sample test statistic? (Test the difference - Round your answer to three decimal places) (c) Frd (or estimate the P-value Puve 0.250 0.125 Avue 0.250 0.050 < P-value < 0.125 0.025 < P ue < 0.050 0.005 < P-value < 0.025 S l ing distribution and show the area corresponding to the value (d) Based on your answers in parts (o) to (c), will you reject or fail to reject the hypothesis? Are the data statistically significant at level At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the e-0.05 level, we reject the us ypothesis and conclude the data are statistically w a nt At the a-0.05 level, we foto reject the null typothesis and conclude the data are statistically significant At the a= 0.05 level, we reject the nut hypothesis and conclude the data are not statistically cant. (e) Interpret your conclusion in the context of the application Fall to reject the null hypothesis, there is insuficient evidence that the moon rate of hayfever slower for the age group over 50 Par to repeat the press, there is wifest evidence that the mean role of the fewer is tower for e t group over 30 Reject the hypothes, there is sufficient evidence that the mean rate of Nayfever is for the age ou verso Reject the will hypothesis, there is incent evidence that the mean rate of h e r for the grader