Answer: 2.5
Step-by-step explanation:
Let be the population mean .
Then, Null hypothesis :
Alternative hypothesis :
We assume that this is a normal distribution.
Given : Sample size : n=25 , since the sample is small (n<30) so we cannot apply z-test . Thus the test is t-test.
Sample mean :
Population standard deviation :
The test statistic for population mean is given by :-
i.e.
Hence, the observed critical value = 2.5
Answer:
The 95% confidence interval to determine the true proportion of all patrons who would be interested in attending the showing is (0.2121, 0.4671).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of .
Of the 53 patrons, 18 said that they would come to see the film.
This means that
95% confidence level
So , z is the value of Z that has a p-value of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval to determine the true proportion of all patrons who would be interested in attending the showing is (0.2121, 0.4671).
