Respuesta :
Answer:
The 95% confidence interval estimate of the population mean rating for Miami is (6.0, 7.5).
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:
[tex]CI=\bar x \pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
The sample selected is of size, n = 50.
The critical value of t for 95% confidence level and (n - 1) = 49 degrees of freedom is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 49}\approx t_{0.025, 60}=2.000[/tex]
*Use a t-table.
Compute the sample mean and sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{50}\times [1+5+6+...+10]=6.76\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{49}\times 31.12}=2.552[/tex]
Compute the 95% confidence interval estimate of the population mean rating for Miami as follows:
[tex]CI=\bar x \pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.76\pm 2.000\times \frac{2.552}{\sqrt{50}}\\\\=6.76\pm 0.722\\\\=(6.038, 7.482)\\\\\approx (6.0, 7.5)[/tex]
Thus, the 95% confidence interval estimate of the population mean rating for Miami is (6.0, 7.5).
