SOLUTION: The winning team's scores in 9 high school basketball games were recorded. If the sample mean is 9.8 points and the sample standard deviation is 0.30 points, find the 98% confidenc

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Question 1039784: The winning team's scores in 9 high school basketball games were recorded. If the sample mean is 9.8 points and the sample standard deviation is 0.30 points, find the 98% confidence interval of the true mean.
A.
(9.70, 9.90)
B.
(9.51, 10.09)
C.
(9.22, 10.38)
D.
(9.57, 10.03)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First use a calculator to find the t critical value.

Use the invT function on your TI83/TI84/etc calculator to get the result of -2.896 approximately (see screenshot below)

The 98% confidence interval will have 100-98 = 2% of the area in the tails. So 2/2 = 1% of the area is in the left tail. The goal is to find the value of k such that P(T < k) = 0.01. So that's why 0.01 is typed in as part of the calculator input (see screenshot below)

The degrees of freedom (df) is df = n-1 = 9-1 = 8. So that explains the 8 as the second input (see screenshot below)





Note: to get the invT function, you hit the blue 2ND key. Then you hit the VARS key. The invT function is at #4.

The positive version of this number is the value we want. So the critical t value is approximately t = 2.896

If you do not have a TI calculator, such as a TI83 or TI84, then you can use a table like this one (often found in the back of your textbook) to find the critical value. Look at the row df = 8. Then find the column that corresponds to the confidence level of 98%. The value 2.896 will be found at this row and column combo.

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Let's compute the lower bound and upper bound. We'll make L be the lower bound and U the upper bound.

We will use these formulas




In this case,
is the sample mean
s = 0.30 is the standard deviation
n = 9 is the sample size
t = 2.896 is the critical value we just found with the calculator
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Let's plug these values in and compute

First let's find the lower bound L







So the lower bound is approximately 9.51

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Now let's find the upper bound U







So the upper bound is approximately 10.09

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To summarize, we found that
L = 9.51
U = 10.09

The 98% confidence interval is therefore (L,U) = (9.51, 10.09)

So the answer is Choice B