In order to conduct a hypothesis test for the population mean, a random sample o
ID: 3130468 • Letter: I
Question
In order to conduct a hypothesis test for the population mean, a random sample of 15 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 8.6 and 1.8, respectively. Use Table 2.
Use the p-value approach to conduct the following tests at = 0.10.
a-1.
Calculate the value of the test statistic. (Round your answer to 2 decimal places.)
a-2.
a-3.
b-1.
Calculate the value of the test statistic. (Round your answer to 2 decimal places.)
b-2.
b-3.
(Round all intermediate calculations to at least 4 decimal places.)Explanation / Answer
a-1.
Formulating the null and alternative hypotheses,
Ho: u <= 7.3
Ha: u > 7.3
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 8.6
uo = hypothesized mean = 7.3
n = sample size = 15
s = standard deviation = 1.8
Thus, t = (X - uo) * sqrt(n) / s = 2.797154639 [ANSWER]
***************************
a-2.
Thus,
df = n - 1 = 14
Also, the p value is using a table,
0.005<p<0.010 [ANSWER, C]
*******************************
a-3.
As P < 0.10, then
OPTION A: Reject H0 since the p-value is less than . [ANSWER]
*****************************
b-1.
Formulating the null and alternative hypotheses,
Ho: u = 7.3
Ha: u =/ 7.3
As we can see, this is a two tailed test.
Getting the test statistic, as
X = sample mean = 8.6
uo = hypothesized mean = 7.3
n = sample size = 15
s = standard deviation = 1.8
Thus, t = (X - uo) * sqrt(n) / s = 2.797154639 [ANSWER]
*******************************
b-2.
Thus,
df = n - 1 = 14
Also, the p value is, using a table,
0.01<p<0.02 [ANSWER, C]
*****************************
b-3.
As P < 0.10,
OPTION D: Reject H0 since the p-value is less than . [ANSWER]
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