Solution Found!
In each of the following instances, determine whether you
Chapter 6, Problem 106SE(choose chapter or problem)
In each of the following instances, determine whether you would use a z- or t-statistic (or neither) to form a 95% confidence interval and then look up the appropriate z- or t-value.
a. Random sample of size n = 23 from a normal distribution with unknown mean μ and standard deviation \(\sigma\)
b. Random sample of size n = 135 from a normal distribution with unknown mean μ and standard deviation \(\sigma\)
c. Random sample of size n = 10 from a normal distribution with unknown mean μ and standard deviation s = 5
d. Random sample of size n = 73 from a distribution about which nothing is known
e. Random sample of size n = 12 from a distribution about which nothing is known
Questions & Answers
QUESTION:
In each of the following instances, determine whether you would use a z- or t-statistic (or neither) to form a 95% confidence interval and then look up the appropriate z- or t-value.
a. Random sample of size n = 23 from a normal distribution with unknown mean μ and standard deviation \(\sigma\)
b. Random sample of size n = 135 from a normal distribution with unknown mean μ and standard deviation \(\sigma\)
c. Random sample of size n = 10 from a normal distribution with unknown mean μ and standard deviation s = 5
d. Random sample of size n = 73 from a distribution about which nothing is known
e. Random sample of size n = 12 from a distribution about which nothing is known
ANSWER:Solution 106SE
Step1 of 6:
From the given problem we have Random sample of size n and with unknown mean and standard deviation
Here our goal is:
a). We need to form a 95% confidence interval random sample of size n = 23 from a normal distribution with unknown mean μ and standard deviation σ.
b). We need to form a 95% confidence interval random sample of size n = 135 from a normal distribution with unknown mean μ and standard deviation σ.
c). We need to form a 95% confidence interval random sample of size n = 10 from a normal distribution with unknown mean μ and standard deviation s = 5.
d). We need to form a 95% confidence interval random sample of size n = 73 from a distribution about which nothing is known.
e). We need to form a 95% confidence interval random sample of size n = 12 from a distribution about which nothing is known.
Step2 of 6:
a).
We know that t-statistics is used For a small sample from a normal distribution with unknown standard deviation. Then,
For a confidence coefficient,
Now,
The t-statistics is:
Where, is obtained from critical value of t distribution table, with 22 degrees of freedom. That is,
Therefore, the value of