Answer:
The degrees of freedom are given by:
And the p value would be given by:
Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.
Step-by-step explanation:
Information given
314 305 344 283 285 310 383 285 300 300
We can calculate the sample mean and deviation with the following formula:
represent the sample mean
represent the standard deviation for the sample
sample size
represent the value to test
represent the significance level
t would represent the statistic
represent the p value
Hypothesis to test
We want to verify if the true mean is greater than 300, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing the info given we got:
The degrees of freedom are given by:
And the p value would be given by:
Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.