Answer:
For the critical value we need to calculate the degrees of freedom given by:
And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value with right arm , y = test value with left arm
The system of hypothesis for this case are:
Null hypothesis: 
Alternative hypothesis: 
The first step is calculate the difference 
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
The 4 step is calculate the statistic given by :
For the critical value we need to calculate the degrees of freedom given by:
And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:
All transportation (bus, cab, train) are all similarly likely to be selected, and 1 of them must be selected at morning and evening, so we get: P (bus) = P (cab) = P (train) = 1/3. We also have P(no cab in evening) = P(no cab at morning) = 2/3
Now, P(using cab exactly once) = P(cab at morning and no cab in the evening) + P(no cab at morning and cab in the evening)
= P(cab, no cab) + P(no cab, cab)
= 1/3 * 2/3 + 2/3 * 1/3
= 2/9 + 2/9
= 4/9
Probability that Elizabeth uses a cab only once is 4/9.
Answer: The required inequality is 
and its solution is 
Step-by-step explanation: Given that Mustafa, Heloise, and Gia have written more than a combined total of 22 articles for the school newspaper.
Also, Heloise has written 
as many articles as Mustafa has and Gia has written 
as many articles as Mustafa has.
We are to write an inequality to determine the number of articles, m, Mustafa could have written for the school newspaper. Also, to solve the inequality.
Since m denotes the number of articles that Mustafa could have written. Then, according to the given information, we have
And the solution of the above inequality is as follows :
Thus, the required inequality is and its solution is
Answer:
Critical value: T = 1.337
The 80% confidence interval for the mean repair cost for the stereos is between $45.991 and $86.689
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 17 - 1 = 16
80% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 16 degrees of freedom(y-axis) and a confidence level of 
. So we have T = 1.337, which is the critical value
The margin of error is:
M = T*s = 1.337*15.22 = 20.349
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 66.34 - 20.349 = $45.991
The upper end of the interval is the sample mean added to M. So it is 66.34 + 20.349 = $86.689
The 80% confidence interval for the mean repair cost for the stereos is between $45.991 and $86.689
