x
2: Rate of hay fever per 1000 population for people over 50
94 |
109 |
103 |
95 |
110 |
88 |
110 |
79 |
115 |
100 |
89 |
114 |
85 |
96 |
(i) Use a calculator to calculate x1,s
1, x2, ands
2. (Round your answers to four decimal places.)
(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.
A-H
0: ?1 = ?2;H
1: ?1 ≠ ?2
B-H
0: ?1 > ?2;H
1: ?1 = ?2
C-H
0: ?1 = ?2;H
1: ?1 > ?2
D-H
0: ?1 = ?2;H
1: ?1 <>2
(b) What sampling distribution will you use? What assumptions are you making?
A-The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
B-The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.
C-The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
D-The Student'st. 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) theP-value.
A-P-value > 0.250
B-0.125 P-value <>
C-0.050 P-value <>
D-0.025 P-value <>
E-0.005 P-value <>
F-P-value <>
Sketch the sampling distribution and show the area corresponding to theP-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 ??
A-At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
B-At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
C-At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
D-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.
A-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.
B-Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.
C-Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.
D-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.