Question
In: Statistics and Probability
Suppose μ1 and μ2 are true mean, for An experiment resulted in the following data: System...
Suppose μ1 and μ2 are true mean, for An experiment resulted in the following data:
System 1: m = 6, Xbar= 115.7, s1= 5.03;
System 2: n = 6, Ybar=129.3, s2= 5.38.
Use the two-sample t test at significance level 0.01 to test H0: μ1- μ2= -10 versus Ha: H0: μ1- μ2 < -10. You can use either critical value or p-value to reach to a conclusion.
Please be as detailed as possible and list any assumptions made. Thank you very much!
Solutions
Expert Solution
Assumptions : Two populations are independent and normally distributed.
orchestra answered 1 year agoRelated Solutions
Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a...
Suppose μ1 and μ2 are
true mean stopping distances at 50 mph for cars of a certain type
equipped with two different types of braking systems. Use the
two-sample t test at significance level 0.01 to test
H0: μ1 −
μ2 = −10 versus Ha:
μ1 − μ2 < −10 for the
following data: m = 6, x = 114.8,
s1 = 5.05, n = 6, y = 129.4,
and s2 = 5.33.
Calculate the test statistic and determine the...
Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a...
Suppose μ1 and μ2 are
true mean stopping distances at 50 mph for cars of a certain type
equipped with two different types of braking systems. Use the
two-sample t test at significance level 0.01 to test
H0: μ1 −
μ2 = −10 versus Ha:
μ1 − μ2 < −10 for the
following data: m = 7, x = 114.5,
s1 = 5.06, n = 7, y = 129.9,
and s2 = 5.38.
Calculate the test statistic and determine the...
Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a...
Suppose μ1 and μ2 are
true mean stopping distances at 50 mph for cars of a certain type
equipped with two different types of braking systems. The data
follows: m = 10, x = 116.8,
s1 = 5.28, n = 7,
y = 129.6, and s2 = 5.47.
Calculate a 99% CI for the difference between true average stopping
distances for cars equipped with system 1 and cars equipped with
system 2. (Give answers accurate to 2 decimal places.)
Lower...
Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a...
Suppose μ1 and μ2 are
true mean stopping distances at 50 mph for cars of a certain type
equipped with two different types of braking systems. The data
follows: m = 8,x = 115.8, s1
= 5.06, n = 8, y = 129.5, and
s2 = 5.35. Calculate a 95% CI for the
difference between true average stopping distances for cars
equipped with system 1 and cars equipped with system 2. (Round your
answers to two decimal places.)
Consider the hypothesis test with null hypothesis μ1=μ2 and alternative hypothesis μ1 > μ2.Suppose that sample...
Consider the hypothesis test with null hypothesis μ1=μ2 and
alternative hypothesis μ1 > μ2.Suppose that sample sizes n1 = 10
and n2 =10, that the sample means are 4.9 and 2.8 respectively, and
that the sample variances are 2 and 3 respectively. Assume that the
population variances are equal and that the data are drawn from
normal distributions.
a) Test the hypothesis that at α= 0.05 and provide a conclusion
statement
b) Provide an adequate confidence interval with 95% confidence...
Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠...
Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 −
μ2 ≠ 0 The following results are from independent samples taken
from two populations assuming the variances are unequal. Sample 1
Sample 2 n1 = 35 n2 = 40 x1 = 13.6 x2 = 10.1 s1 = 5.8 s2 = 8.2
(a) What is the value of the test statistic? 2.153 correct
(b) What is the degrees of freedom for the t distribution?
(Round your answer...
Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠...
Consider the following hypothesis test.
H0: μ1 − μ2 = 0
Ha: μ1 − μ2 ≠ 0
The following results are from independent samples taken from
two populations.
Sample 1
Sample 2
n1 = 35
n2 = 40
x1 = 13.6
x2 = 10.1
s1 = 5.9
s2 = 8.1
(a)
What is the value of the test statistic? (Use
x1 − x2.
Round your answer to three decimal places.)
(b)
What is the degrees of freedom for the t...
Consider the following ANOVA experiment: H0: μ1 = μ2 = μ3 = μ4 with n =...
Consider the following ANOVA experiment:
H0: μ1 =
μ2 = μ3 =
μ4
with
n = 21,
a sample F statistic = 4.76, and
α = 0.025.
You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1≠μ2H1:μ1≠μ2...
You wish to test the following claim (H1H1) at a significance
level of α=0.001α=0.001.
Ho:μ1=μ2Ho:μ1=μ2
H1:μ1≠μ2H1:μ1≠μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. However, you also have
no reason to believe the variances of the two populations are not
equal. You obtain a sample of size n1=24n1=24 with a mean of
M1=85.8M1=85.8 and a standard deviation of SD1=19.3SD1=19.3 from
the first population. You obtain a sample of size n2=17n2=17 with...
You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1>μ2H1:μ1>μ2...
You wish to test the following claim (H1H1) at a significance
level of α=0.02α=0.02.
Ho:μ1=μ2Ho:μ1=μ2
H1:μ1>μ2H1:μ1>μ2
You obtain the following two samples of data.
Sample #1
Sample #2
97.7
78.7
14.7
91.3
90.1
39.8
56.9
47.2
67.5
62.3
64.9
26.7
79.4
52.9
63.3
69.1
20.4
67.5
54.1
67
46.4
52.3
44.2
65.9
95.8
56.9
78.7
85.9
56.4
59.1
53.5
72.5
70.8
61.2
64.9
70.2
68.6
44.2
41.6
77.4
81.6
14.7
55.2
71.4
56.4
50.5
52.9
41.6
24
49.9
53.5
74.9...
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