In: Statistics and Probability
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).
H0: μ ≤ 13.0 against
HA: 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? Which one.
_Reject H0 since the p-value is less than significance level.
_Reject H0 since the p-value is greater than significance level.
_Do not reject H0 since the p-value is less than significance level.
_Do not reject H0 since the p-value is greater than significance level.
a-4. Interpret the results at αα = 0.01. Which
one.
_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.
H0: μ = 13.0 against HA: 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? Which one.
_Reject H0 since the p-value is less than significance level.
_Reject H0 since the p-value is greater than significance level.
_Do not reject H0 since the p-value is less than significance level.
_Do not reject H0 since the p-value is greater than significance level.
b-4. Interpret the results at αα = 0.01. Which
one
_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
H0 : μ = 13
HA : 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 H0 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 H0 since the p-value is less than significance level.
b - 4) We conclude that the population mean differs from 13.