alphaequals=0.05 H0: 120 H1: 12<0 a) Calculate the appropriate test statistic an
ID: 3221716 • Letter: A
Question
alphaequals=0.05
H0: 120
H1: 12<0
a) Calculate the appropriate test statistic and interpret the result.
b) Calculate the p-value and interpret the result.
overbarx1
=
120
overbarx2
=
136
sigma1
=
38
sigma2
=
34
n1
=
35
n2
=
55
a) The test statistic is
(Round to two decimal places as needed.)
Determine the appropriate critical value(s).
The critical value(s) is(are)
(Round to
three
decimal places as needed. Use a comma to separate answers as needed.)Since the test statistic
falls
does not fall
in the rejection region,
reject
do not reject
Upper H 0H0.
There is
sufficient
insufficient
evidence to conclude that the mean of population 1 is less than the mean of population 2.
b) The p-value is
(Round to three decimal places as needed.)
Since the p-value is
greater than
equal to
less than
alpha,
do not reject
reject
Upper H 0H0.
There is
sufficient
insufficient
evidence to conclude that the mean of population 1 is less than the mean of population 2
Consider the hypothesis statement shown below usingalphaequals=0.05
and the data to the right from two independent samples.H0: 120
H1: 12<0
a) Calculate the appropriate test statistic and interpret the result.
b) Calculate the p-value and interpret the result.
overbarx1
=
120
overbarx2
=
136
sigma1
=
38
sigma2
=
34
n1
=
35
n2
=
55
Explanation / Answer
The statistical software output for this problem is:
Two sample Z hypothesis test:
1 : Mean of population 1 (Std. dev. = 38)
2 : Mean of population 2 (Std. dev. = 34)
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 < 0
Hypothesis test results:
Hence,
a) Test statistic = -2.03
Critical value for a left tailed test with 0.05 level of significance = -1.645
Since the test statistic falls in the rejection region, reject Ho.
There is sufficient evidence to conclude that the mean of population 1 is less than the mean of population 2.
b) p - value = 0.021
Since the p - value is less than alpha , reject Ho.
There is sufficient evidence to conclude that the mean of population 1 is less than the mean of population 2.
Difference n1 n2 Sample mean Std. err. Z-stat P-value 1 - 2 35 55 -16 7.8914716 -2.0275052 0.0213Related Questions
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