Answer:
The value of the test statistic is
Step-by-step explanation:
The formula for the test statistic is:
In which X is the statistic, is the mean,
is the standard deviation and n is the number of observations.
In this problem, we have that:
So
The value of the test statistic is
Answer:
we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613
Step-by-step explanation:
The estimated proportion of interest is
We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by and
.
And the critical value is:
The confidence interval for the true population proportion is interest is given by this formula:
Replacing the values provided we got:
And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613