complete all please! Sample Size level One-tailed or two-tailed t* z* 3 0.05 Two
ID: 3175376 • Letter: C
Question
complete all please!
Sample Size
level
One-tailed or two-tailed
t*
z*
3
0.05
Two-tailed
4.3
1.96
7
0.01
One-tailed
3.14
2.33
10
0.10
One-tailed
1.37
1.28
17
0.01
One-tailed
2.58
2.33
30
0.10
Two-tailed
1.70
1.28
101
0.05
Two-tailed
1.98
1.96
1.Find the values of the t-distribution that bound the middle 0.95 of the area under the curve for the distribution with df = 20. (2 points)
2.Salaries in the NBA are very complicated, with some caps in place. However, even with limits being placed on salaries some players still receive significant salaries. Andrew Wiggins received an $11.2 million contract with the Cleveland Cavaliers, and Jabari Parker has an approximate possible salary of $10.1 with the Milwaukee Bucks. Suppose a random sample of 26 NBA players report their potential annual income at the start of the 2014 season and the results show a mean of $4.8 million and a standard deviation of $2.6 million. (information courtesy of http://www.spotrac.com/draft-tracker/nba)
A.Estimate with 95% confidence the mean of the annual income based on the report. (Specify the population parameter of interest, the conditions, the sample evidence, and the interval limits). (10 points)
Sample Size
level
One-tailed or two-tailed
t*
z*
3
0.05
Two-tailed
4.3
1.96
7
0.01
One-tailed
3.14
2.33
10
0.10
One-tailed
1.37
1.28
17
0.01
One-tailed
2.58
2.33
30
0.10
Two-tailed
1.70
1.28
101
0.05
Two-tailed
1.98
1.96
Explanation / Answer
Solution
Q1
Since t-distribution is symmetric, P(- a < t < a) = 2P(0 < t < a).
So, what we require is: P(- a < t < a) = 0.95 or P(0 < t < a) = 0.475.
Using Excel Function, a = 2.086 for DF = 20
So, the bound is (- 2.086, 2.086) ANSWER
Q2A
100(1 – ) % confidence interval for mean µ when 2 is unknown is: {Xbar ± (s/n)(t/2)}, where
Xbar = sample mean,
= population standard deviation,
s = sample standard deviation,
n = sample size and
t/2 = upper (/2) % point of t-Distribution with (n - 1) degrees of freedom..
Given, n = 26, = 0.05, Xbar = 4.8, s = 2.6, and t25, 0.025= 2.060, [using Excel Function],
95% Confidence Interval for µ is: [4.8 ± {(2.6/(26)}(2.060) =4.8 ± 1.05
Lower Bound = 3.75, Upper Bound = 5.85 ANSWER
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