Consider the following hypothesis statement using =0.10 and data from two indepe
ID: 3364386 • Letter: C
Question
Consider the following hypothesis statement using =0.10 and data from two independent samples. Assume the population variances are equal and the populations are normally distributed. Complete parts a and b
H0: 12=0
H1: 120
x1=14.5
x2=12.0
s1=2.7
s2=3.1
n1=20
n2=16
a. Calculate the appropriate test statistic and interpret the result.
The test statistic is:
(Round to two decimal places as needed.)
The critical value(s) is(are):
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Because the test statistic:
is less than the critical value,
falls within the critical values,
is greater than the critical value,
does not fall within the critical values,
do not reject
reject
the null hypothesis.
b. Identify the p-value from part a and interpret the result.
The p-value is:
(Round to three decimal places as needed.)
Interpret the result. Choose the correct answer below.
A.
Since the p-value is
not lessnot less
than the significance level,
rejectreject
the null hypothesis.
B.
Since the p-value is
lessless
than the significance level,
rejectreject
the null hypothesis.
C.
Since the p-value is
not lessnot less
than the significance level,
do not rejectt
the null hypothesis.
D.
Since the p-value is
less
than the significance level,
do not reject
the null hypothesis.
Click to select your answer(s).
Explanation / Answer
The statistical software output for this problem is:
Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(with pooled variances)
Hypothesis test results:
Hence,
Test statistic = 2.59
Critical values = -1.69, 1.69
Because the test statistic does not fall within the critical values, reject the null hypothesis.
p - value = 0.014
Since the p-value is less than the significance level, reject the null hypothesis.
Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 2.5 0.96709465 34 2.5850624 0.0142Related Questions
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