# A random sample of n1 = 16 com

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

 97 91 122 130 94 123 112 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

 94 111 100 95 110 88 110 79 115 100 89 114 85 96

(i) Use a calculator to calculate x1s1, x2, and s2. (Round your answers to four decimal places.)

 x1 = s1 = x2 = s2 =

# A random sample of n1 = 16 com

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

 97 91 122 130 94 123 112 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

 94 111 100 95 110 88 110 79 115 100 89 114 85 96

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

# A random sample of n1 = 16 com

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

 100 92 122 127 93 123 112 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

 93 112 100 97 111 88 110 79 115 100 89 114 85 96

State the null and alternate hypotheses.

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

What sampling distribution will you use? What assumptions are you making?

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.

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.

What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to three decimal places.)

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

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 not statistically significant.

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 statistically significant.

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

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 com

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

 100 92 121 129 93 123 112 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

 93 108 103 98 112 88 110 79 115 100 89 114 85 96

(i) Use a calculator to calculate x1s1, x2, and s2. (Round your answers to four decimal places.)

 x1 = s1 = x2 = s2 =

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

 100 92 121 129 93 123 112 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

 93 108 103 98 112 88 110 79 115 100 89 114 85 96

(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

(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 α?

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

(e) Interpret your conclusion in the context of the application.

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.
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.
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.

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