Respuesta :
Answer:
a) The parameter of interest on this case is [tex] \mu[/tex] who represent the average number of students in order to create an app.
b) [tex]3.85 - 2.09 \frac{1.348}{\sqrt{20}}=3.22[/tex]
[tex]3.85 + 2.09 \frac{1.348}{\sqrt{20}}=4.48[/tex]
The 95% confidence interval is given by (3.22;4.48)
c) For this case we have 95% of confidence that the true mean for the average number of students in order to create an app is between 3,22 and 4.48.
d) We have the following criteria in order to decide: "You determine that if more than three students share a ride, on average, you will create the app"
So then since the lower limti for the confidence interval is higher than 3 we can conclude that at 5% of significance we have more than 3 students share a ride so then makes sense create the app.
Step-by-step explanation:
Part a
The parameter of interest on this case is [tex] \mu[/tex] who represent the average number of students in order to create an app.
Part b
Data: 6 5 5 5 3 2 3 6 2 2 5 4 3 3 4 2 5 3 4 5
n=20 represent the sample size
[tex]\bar X[/tex] represent the sample mean
[tex]s[/tex] represent the sample standard deviation
m represent the margin of error
Confidence =95% or 0.95
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".
Calculate the mean and standard deviation for the sample
On this case we need to find the sample standard deviation with the following formula:
[tex]s=sqrt{\frac{\sum_{i=1}^20 (x_i -\bar x)^2}{n-1}}[/tex]
And in order to find the sample mean we just need to use this formula:
[tex]\bar x =\frac{\sum_{i=1}^{20} x_i}{n}[/tex]
The sample mean obtained on this case is [tex]\bar x= 3.85[/tex] and the deviation s=1.348
Calculate the critical value tc
In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. The degrees of freedom are given by:
[tex]df=n-1=20-1=19[/tex]
We can find the critical values in excel using the following formulas:
"=T.INV(0.025,19)" for [tex]t_{\alpha/2}=-2.09[/tex]
"=T.INV(1-0.025,19)" for [tex]t_{1-\alpha/2}=2.09[/tex]
The critical value [tex]tc=\pm 2.09[/tex]
Calculate the confidence interval
The interval for the mean is given by this formula:
[tex]\bar X \pm t_{c} \frac{s}{\sqrt{n}}[/tex]
And calculating the limits we got:
[tex]3.85 - 2.09 \frac{1.348}{\sqrt{20}}=3.22[/tex]
[tex]3.85 + 2.09 \frac{1.348}{\sqrt{20}}=4.48[/tex]
The 95% confidence interval is given by (3.22;4.48)
Part c
For this case we have 95% of confidence that the true mean for the average number of students in order to create an app is between 3.22 and 4.48.
Part d
We have the following criteria in order to decide: "You determine that if more than three students share a ride, on average, you will create the app"
So then since the lower limti for the confidence interval is higher than 3 we can conclude that at 5% of significance we have more than 3 students share a ride so then makes sense create the app.
The parameter used in the probability is the average number of students represented by u.
How to calculate the probability?
The confidence interval based on the information will be:
= 3.85 - 2.09(1.348 / ✓20)
= 3.22
Also, 3.85 + 2.09(1.348 / ✓20) = 4.48
The confidence interval simply means that one is 95% confident that the true mean is between 3.22 and 4.48.
Learn more about probability on:
https://brainly.com/question/24756209
