Respuesta :
Answer:
[tex] (26.99-35.76) -1.98 \sqrt{\frac{4.89^2}{68} +\frac{6.43^2}{74}} =-10.659[/tex]
[tex] (26.99-35.76) +1.98 \sqrt{\frac{4.89^2}{68} +\frac{6.43^2}{74}} =-6.88[/tex]
Step-by-step explanation:
For this case we assume the following data:
7-day old: n_1 = 68 x_1 = 26.99 s_1 = 4.89
28-day old: n_2 = 74 x_2 = 35.76 s_2 = 6.43
Previous concepts Â
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". Â
The margin of error is the range of values below and above the sample statistic in a confidence interval. Â
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". Â
Solution to the problem
For this case the confidence interval is given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]
The degrees of freedom are given by:
[tex] df=n_1 +n_2 -2= 68+74-2 = 140[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,140)".And we see that [tex]z_{\alpha/2}=1.98[/tex]
And replaicing we got:
[tex] (26.99-35.76) -1.98 \sqrt{\frac{4.89^2}{68} +\frac{6.43^2}{74}} =-10.659[/tex]
[tex] (26.99-35.76) +1.98 \sqrt{\frac{4.89^2}{68} +\frac{6.43^2}{74}} =-6.88[/tex]
