Respuesta :
Answer:
The 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).
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}=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 [6+4+6+...+9+6]=6.34\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{50-1}\times 229.22}=2.163[/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]=6.34\pm 2.00\times\frac{2.163}{\sqrt{50}}\\\\=6.34\pm 0.612\\\\=(5.728, 6.952)\\\\\approx(5.7, 7.0)[/tex]
Thus, the 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).
