In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 4.8 and 0.8, respectively. (You may find it useful to reference the appropriate table: z table or t table)
H_{0}: μ ≤ 4.5 against H_{A}: μ > 4.5
a-1. Calculate the value of the
test statistic. (Round all intermediate calculations to at
least 4 decimal places and final answer to 3 decimal
places.)
a-2. Find the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
a-3. At the 5% significance level, what is the conclusion?
Reject H_{0} since the p-value is less than α.
Reject H_{0} since the p-value is greater than α.
Do not reject H_{0} since the p-value is less than α.
Do not reject H_{0} since the p-value is greater than α.
a-4. Interpret the results at αα
= 0.05.
We conclude that the population mean is greater than 4.5.
We cannot conclude that the population mean is greater than 4.5.
We conclude that the population mean differs from 4.5.
We cannot conclude that the population mean differs from 4.5.
H_{0}: μ = 4.5 against H_{A}: μ ≠ 4.5
b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
b-2. Find the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
b-3. At the 5% significance level, what is the conclusion?
Reject H_{0} since the p-value is less than α.
Reject H_{0} since the p-value is greater than α.
Do not reject H_{0} since the p-value is less than α.
Do not reject H_{0} since the p-value is greater than α.
b-4. Interpret the results at αα
= 0.05.
We conclude that the population mean is greater than 4.5.
We cannot conclude that the population mean is greater than 4.5.
We conclude that the population mean differs from 4.5.
We cannot conclude that the population mean differs from 4.5.
a-1)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (4.8 - 4.5)/(0.8/sqrt(24))
t = 1.837
a-2)
p-value = P(t > 1.837)
0.025 ≤ p-value < 0.05
a-3.
Reject H0 since the p-value is less than α.
a-4)
We conclude that the population mean is greater than 4.5
b-1)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (4.8 - 4.5)/(0.8/sqrt(24))
t = 1.837
b-2)
p-value = 2*P(t > 1.837)
0.05 ≤ p-value < 0.10
b-3)
Do not reject H0 since the p-value is less than α.
b-4)
We cannot conclude that the population mean differs from
4.5.
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