Respuesta :
Answer:
The 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities is (-1.77, 0.29).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two population mean is:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n-1)}\cdot\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}[/tex]
Compute the value of sample means and sample standard deviations from the provided data.
[tex]\bar x_{1}=3.142\\\\\bar x_{2}=3.882\\\\s_{1}=0.4396\\\\s_{2}=0.4283\\n_{1}=n_{2}=5[/tex]
The critical value of t for 98% confidence level and (n - 1) = 4 degrees of freedom is:
[tex]t_{\alpha/2, (n-1)}=t_{0.02/2, 4}=3.747[/tex]
Compute the 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities as follows:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n-1)}\cdot\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}[/tex]
[tex]=(3.142-3.882)\pm3.747\cdot\sqrt{\frac{0.4396^{2}}{5}+\frac{0.4283^{2}}{5}}\\\\=-0.74\pm 1.0285\\\\=(-1.7685, 0.2885)\\\\\approx (-1.77, 0.29)[/tex]
Thus, the 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities is (-1.77, 0.29).
