Answer:
Null hypothesis:
Alternative hypothesis:
And we want to test this with a confidence interval:
The confidence interval for the mean is given by the following formula:
(1)
After conduct the interval of 95% for the true mean we got: (11.59, 13.31)
And for this case the confidence interval contains the value of 11.89, so then we have enough evidence to FAIL to reject the null hypothesis at 5% of significance that the true mean is 11.89.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n=30 represent the sample size
Solution to the problem
For this case we want to test the following hypothesis:
Null hypothesis:
Alternative hypothesis:
And we want to test this with a confidence interval:
The confidence interval for the mean is given by the following formula:
(1)
After conduct the interval of 95% for the true mean we got: (11.59, 13.31)
And for this case the confidence interval contains the value of 11.89, so then we have enough evidence to FAIL to reject the null hypothesis at 5% of significance that the true mean is 11.89.