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 99 92 122 127 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 93 108 100 96 112 88 110 79 115 100 89 114 85 96 (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to four 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 ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 > ?2H0: ?1 = ?2; H1: ?1 < ?2 H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 > ?2; H1: ?1 = ?2 (b) What sampling distribution will you use? What assumptions are you making? 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 unknown 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 ?1 − ?2. 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. (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 ?? At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 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. 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.Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50. Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.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.

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 99 92 122 127 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 93 108 100 96 112 88 110 79 115 100 89 114 85 96 (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to four 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 ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 > ?2H0: ?1 = ?2; H1: ?1 < ?2 H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 > ?2; H1: ?1 = ?2 (b) What sampling distribution will you use? What assumptions are you making? 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 unknown 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 ?1 − ?2. 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. (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 ?? At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 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. 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.Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50. Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

99	92	122	127	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

93	108	100	96	112	88	110
79	115	100	89	114	85	96

(i) Use a calculator to calculate x₁, s₁, x₂, and s₂. (Round your answers to four 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 ? = 0.05.
(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: ?₁ = ?₂; H₁: ?₁ > ?₂H₀: ?₁ = ?₂; H₁: ?₁ < ?₂ H₀: ?₁ = ?₂; H₁: ?₁ ≠ ?₂H₀: ?₁ > ?₂; H₁: ?₁ = ?₂

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

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 unknown 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 ?₁ − ?₂. 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.

(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 ??

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 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.

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.Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50. Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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