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 96 92 119 127 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 94 109 99 96 110 88 110 79 115 100 89 114 85 96

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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
96 92 119 127 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
94 109 99 96 110 88 110
79 115 100 89 114 85 96

 

I need help with (c), sketching, (d) and (e)

 

Sketch the sampling distribution and show the area corresponding to the P-value.
a
b
P-value
P-value
-t
d
P-value
P-value
-t
t
t
(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 a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 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.
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.
O Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 5o.
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.
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. a b P-value P-value -t d P-value P-value -t t t (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 a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a = 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. 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. O Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 5o. 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.
A random sample of n, = 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
96 92 119
127 93 123 112 93
125 95
125
117 97
122 127 88
A random sample of n, = 14 regions in western Kansas gave the following information for people over 50 years old.
x3: Rate of hay fever per 1000 population for people over 50
94
109
99 96 110 88 110
79
115
100 89 114 85
96
In USE SALT
(i) Use a calculator to calculate x,, s1, X2, and s,. (Round your answers to four decimal places.)
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 a = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: H1 = H2i Hz: H1 < Hz
O Ho: H1 > Hzi Hi: Hy = H2
O Ho: H1 = H2i Hz: H1 > H2
O Ho: H1 = H2i H;: H1 # Hz
(b) What sampling distribution will you use? What assumptions are you making?
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 known 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 u, - µ3. Round your answer to three decimal places.)
Transcribed Image Text:A random sample of n, = 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 96 92 119 127 93 123 112 93 125 95 125 117 97 122 127 88 A random sample of n, = 14 regions in western Kansas gave the following information for people over 50 years old. x3: Rate of hay fever per 1000 population for people over 50 94 109 99 96 110 88 110 79 115 100 89 114 85 96 In USE SALT (i) Use a calculator to calculate x,, s1, X2, and s,. (Round your answers to four decimal places.) 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 a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 = H2i Hz: H1 < Hz O Ho: H1 > Hzi Hi: Hy = H2 O Ho: H1 = H2i Hz: H1 > H2 O Ho: H1 = H2i H;: H1 # Hz (b) What sampling distribution will you use? What assumptions are you making? 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 known 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 u, - µ3. Round your answer to three decimal places.)
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