If you could explain it a little, or just use enough detailed so I know how you
ID: 3238098 • Letter: I
Question
If you could explain it a little, or just use enough detailed so I know how you got your figures. basically show your work so I can follow along and understand this.
A father is concerned that his teenage son is watching too much television each day, since his son watches an average of 2 hours per day. His son says that his TV habits are no different than those of his friends. Since this father has taken a stats class, he knows that he can actually test to see whether or not his son is watching more TV than his peers. The father collects a random sample of television watching times from boys at his son's high school and gets the following data:
http://www.statcrunch.com/app/index.php?dataid=1845131
Is the father right? Perform a hypothesis test (by hand) to check the father's claim that other boys average less than 2 hours of television per day. Include the following:
State the null and alternative hypotheses in symbols and words Assume conditions are met. (2 pts)
Perform your hypothesis test calculations "by hand" using the equation editor. Be sure to include the correct probability notation. (4 pts)
Find the corresponding confidence interval "by hand" using the equation editor. (4 pts)
State your conclusion, making sure to site whether we reject or fail to reject and what that means in context. Include the results from your confidence interval. Be sure to tell whether our hypothesized value falls in the interval, and what that tells us. (3 pts)
1.9 2.3 2.2 1.9 1.6 2.6 1.4 2.0 2.0 2.2 A father is concerned that his teenage son is watching too much television each day, since his son watches an average of 2 hours per day. His son says that his TV habits are no different than those of his friends. Since this father has taken a stats class, he knows that he can actually test to see whether or not his son is watching more TV than his peers. The father collects a random sample of television watching tines fron boys at his son's high school and gets the following data: 1.9 2.3 2.2 1.9 1.6 2.6 1.4 2.0 2.0 2.2 htt con/a Vindex dataid-1845131 ls the father right? Perform a hypothesis test (by hand) to check the fathers claim that other boys average less than 2 hours of television per day. Include the following 1. State the null and alternative hypotheses in symbols and words Assume conditions are met. (2 pts) 2. Perform your hypothesis test calculations by hand using the equation editor. Be sure to include the correct probability notation. (4 pts) 3. Find the corresponding confidence interval by hand" using the equation editor. (4 pts) 4. State your conclusion, making sure to site whether we reject or fail to reject and what that means in context. Include the results from your confidence interval. Be sure to tell whether our hypothesized value falls in the interval, and what that tells us. (3 pts)Explanation / Answer
let X denotes the television watching times of boy's at his son's high school. ( in hours)
assumption is that X~N(u,sigma2) where the parameters are unknown.
level of significance=alpha=0.05
his father collects a random sample of size=n=10
the father claims that other boys average less than 2 hours of television per day.
1. so the null hypothesis is
H0: u=2 in words, H0: the average television watching time of boys of the high school is 2 hours per day
alternative hypothesis is
H1: u<2 in words, H0: the average television watching time of boys of the high school is less than 2 hours per day
2. to test the above hypothesis we have a random sample of size=n=10 with sample mean
xbar=(1.9+2.3+...+2.2)/10=2.010 and sample standard deviation=s=sqrt(s2)
where s2=[(1.9-2.01)2+(2.3-2.01)2+...+(2.2-2.01)2]/(10-1)=0.119
so s=sqrt(0.119)=0.345
the test statistic is given by T=(xbar-2)*sqrt(n)/s which under H0 follows a t distribution with n-1 degrees of freedom
since the alternative hypothesis is less than type hence H0 is rejected iff t<-talpha;n-1 where t is the observed value of T and talpha;n-1 is the upper alpha point of a t distribution with df n-1
now t=(2.01-2)*sqrt(10)/0.345=0.09166022
and -t0.05;9=-1.833113
so t>-t0.05;9 hence we fail to reject H0
3. now we need to find a 95% confidence interval for the population mean u
we know T=(xbar-u)*sqrt(n)/s follows a t distribution with n-1 degrees of freedom
so P[|T|>talpha/2;n-1]=1-alpha
or, P[|(xbar-u)*sqrt(n)/s|>t0.025;9]=0.95
or, P[xbar-s*t0.025;9/sqrt(n)<u<xbar+s*t0.025;9/sqrt(n)]=0.95
hence the 95% confidence interval of u is
[xbar-s*t0.025;9/sqrt(n),xbar+s*t0.025;9/sqrt(n)]=[2.01-2.262157*0.345/sqrt(10),2.01+2.262157*0.345/sqrt(10)]
=[1.763202,2.256798] [answer]
4. so on the basis of hyppothesis texting H0 is accepted at 5% level of significance . so the conclusion is that the father's claim that other boys average less than 2 hours of television per day is false
on the basis of confidence interval at 5% level of significance H0 is accepted because the confidence interval contains the null hypothesized value of u. so the conclusion is that the father's claim that other boys average less than 2 hours of television per day is false