Independent random samples from two normal populations produced the variances li
ID: 3155307 • Letter: I
Question
Independent random samples from two normal populations produced the variances listed here.
(a) Do the data provide sufficient evidence to indicate that 12 differs from 22? Test using = 0.05. (Round your answers to two decimal places.)
1-2. Null and alternative hypotheses:
A) H0: 12 22 versus Ha: 12 = 22
B) H0: 12 = 22 versus Ha: 12 < 22
C) H0: 12 = 22 versus Ha: 12 22
D) H0: 12 < 22 versus Ha: 12 > 22
E) H0: 12 = 22 versus Ha: 12 > 22
3. Test statistic: F = _____
5. Conclusion:
A) H0 is not rejected. There is insufficient evidence to indicate that 12 differs from 22.
B) H0 is rejected. There is insufficient evidence to indicate that 12 differs from 22.
C) H0 is not rejected. There is sufficient evidence to indicate that 12 differs from 22.
D) H0 is rejected. There is sufficient evidence to indicate that 12 differs from 22.
(PART B) Find the approximate p-value for the test.
A) p-value < 0.010
B) 0.010 < p-value < 0.020
C) 0.020 < p-value < 0.050
D) 0.050 < p-value < 0.100
E) 0.100 < p-value < 0.200
F) p-value > 0.200
Interpret its value.
A) Since the p-value is less than 0.05, there is sufficient evidence to indicate that 12 differs from 22.
B) Since the p-value is not less than 0.05, there is sufficient evidence to indicate that 12 differs from 22.
C) Since the p-value is not less than 0.05, there is insufficient evidence to indicate that 12 differs from 22.
D) Since the p-value is less than 0.05, there is insufficient evidence to indicate that 12 differs from 22.
Sample Size Sample Variance 21 53.7 23 33.2Explanation / Answer
1-2.
Formulating the null and alternative hypotheses,
OPTION C) H0: 12 = 22 versus Ha: 12 22 [ANSWER]
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3.
As we can see, this is a two tailed test.
Getting the test statistic, as
s1^2 = 53.7
s2^2 = 33.2
Thus, F = s1^2/s2^2 = 1.61746988 [ANSWER]
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5.
Thus, getting the critical F, as alpha = 0.05 ,
alpha/2 = 0.025
df1 = n1 - 1 = 20
df2 = n2 - 1 = 22
F (crit) = 0.410901531 and 2.388982853
As F is between the two critical values, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence,
A) H0 is not rejected. There is insufficient evidence to indicate that 12 differs from 22. [ANSWER, A]
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b)
F) p-value > 0.200 [ANSWER]
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C) Since the p-value is not less than 0.05, there is insufficient evidence to indicate that 12 differs from 22. [ANSWER]