The one-sample t statistic from a sample of n =26 observations for the two-sided
ID: 3254564 • Letter: T
Question
The one-sample t statistic from a sample of n=26 observations for the two-sided test of
H0:=64
Ha0:64
has the value t=1.07
(a) What are the degrees of freedom for t?
df =
(b) What are the two-sided P-value (±0.0001) (Use software)
P =
(c) Is the value t=1.07 statistically significant at the 10% level?
NOTE: The numerical values in this problem have been modified for testing purposes.The one-sample t statistic from a sample of n=26 observations for the two-sided test of
H0:=64
Ha0:64
has the value t=1.07
(a) What are the degrees of freedom for t?
df =
(b) What are the two-sided P-value (±0.0001) (Use software)
P =
(c) Is the value t=1.07 statistically significant at the 10% level?
t=1.07 is not significant at =0.1 t=1.07 is significant at =0.1Explanation / Answer
Solution:-
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 64
Alternative hypothesis: 64
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a one-sample t-test.
Analyze sample data.
Given, t = 1.07
n = 26
df = n - 1 = 26 - 1 = 25
Since we have a two-tailed test, the P-value is the probability that the t statistic having 25 degrees of freedom is less than -1.07 or greater than 1.07.
We use the t Distribution Calculator to find P(t < -1.07)
The P-Value is 0.294842.
The result is not significant at p < 0.10.
Interpret results. Since the P-value (0.29) is greater than the significance level (0.10), we cannot reject the null hypothesis.
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