Respuesta :
Answer:
a) The 90% confidence interval would be given by (721.716;790.724)
b) We are 90% confident that the true mean for the true speed of light is between (721.716;790.724)
c) We assume the following conditions:
- Randomization
- Independence
- Deviation unknown [tex]\sigma[/tex]
Step-by-step explanation:
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".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
Part a
[tex]\bar X=756.22[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]s=100.89[/tex] represent the sample standard deviation
n=25 represent the sample size
90% confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,24)".And we see that [tex]t_{\alpha/2}=1.71[/tex]
Now we have everything in order to replace into formula (1):
[tex]756.22-1.71\frac{100.89}{\sqrt{25}}=721.716[/tex]
[tex]756.22+1.71\frac{100.89}{\sqrt{25}}=790.724[/tex]
So on this case the 90% confidence interval would be given by (721.716;790.724)
Part b
We are 90% confident that the true mean for the true speed of light is between (721.716;790.724)
Part c
We assume the following conditions:
- Randomization
- Independence
- Deviation unknown [tex]\sigma[/tex]
