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 13.9 and 1.6, respectively. (You may find it useful to reference the appropriate table: z table or t table).
H_{0}: μ ≤ 13.0 against H_{A}: μ > 13.0
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
a-3. At the 1% significance level, what is the conclusion?
Reject H_{0} since the p-value is less than significance level.
Reject H_{0} since the p-value is greater than significance level.
Do not reject H_{0} since the p-value is less than significance level.
Do not reject H_{0} since the p-value is greater than significance level.
a-4. Interpret the results at αα = 0.01.
We conclude that the population mean is greater than 13.
We cannot conclude that the population mean is greater than 13.
We conclude that the population mean differs from 13.
We cannot conclude that the population mean differs from 13.
H_{0}: μ = 13.0 against H_{A}: μ ≠ 13.0
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
b-3. At the 1% significance level, what is the conclusion?
Reject H_{0} since the p-value is less than significance level.
Reject H_{0} since the p-value is greater than significance level.
Do not reject H_{0} since the p-value is less than significance level.
Do not reject H_{0} since the p-value is greater than significance level.
b-4. Interpret the results at αα = 0.01.
We conclude that the population mean is greater than 13.
We cannot conclude that the population mean is greater than 13.
We conclude that the population mean differs from 13.
We cannot conclude that the population mean differs from 13.
The statistical software output for this problem is:
One sample T summary hypothesis test:
μ : Mean of population
H_{0} : μ = 13
H_{A} : μ > 13
Hypothesis test results:
Mean | Sample Mean | Std. Err. | DF | T-Stat | P-value |
---|---|---|---|---|---|
μ | 13.9 | 0.32659863 | 23 | 2.755676 | 0.0056 |
Hence,
a - 1) Test statistic = 2.756
a - 2) p-value < 0.01
a - 3) Reject H_{0} since the p-value is less than significance level.
a - 4) We conclude that the population mean is greater than 13.
b - 1) Test statistic = 2.756
b - 2) p-value < 0.01
b - 3) Reject H_{0} since the p-value is less than significance level.
b - 4) We conclude that the population mean differs from 13.
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