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R8.5. Smart kids A school counselor wants to know how smart the students in her school are. She gets funding from the principal to give an IQ test to an SRS of 60of the over 1000students in the school. The mean IQ score was 114.98and the standard deviation was 14.80.
(a) Describe the parameter in this setting.
(b) Explain why the Normal condition is met in this case.
(c) Construct a 90% confidence interval for the mean IQ score of students at the school.
(d) Interpret your result from part (c) in context.

Short Answer

Expert verified

(a) The parameter displays the population mean, which displays the average IQ score of all students enrolled in school.

(b) Because the sample size of 60is greater than 30, the Normal condition is satisfied, and the sample distribution can be presumed to be approximately normal.
(c) The confidence interval is (111.79,118.17).

(d) There is a 90%confident that the genuine mean IQ score of the students will fall somewhere between 111.79and 118.17.

Step by step solution

01

Part (a) Step 1: Given information

To describe the parameter in this setting.

02

Part (a) Step 2: Explanation

Let, the sample mean is (x)=114.98.
The sample standard deviation is (s)=14.80.
And the Sample size is (n)=60.
The confidence interval is calculated as:
x-t/2sn<<x+t/2sn
The parameter displays the population mean, which displays the average IQ score of all students enrolled in school.

03

Part (b) Step 1: Given information

To explain that why the Normal condition is met in this case.

04

Part (b) Step 2: Explanation

The sample size must be more than 30 to satisfy the normalcy criteria.
The sample size in this case is 60, which is higher than 30.
As a result, the criteria of normality is met.

05

Part (c) Step 1: Given information

To construct a 90%confidence interval for the mean IQ score of students at the school.

06

Part (c) Step 2: Explanation

Using a Ti-83 calculator, the following confidence interval was calculated:

As a result, the confidence interval is (111.79,118.17).

07

Part (d) Step 1: Given information

To interpret your result from part (c) in context.

08

Part (a) Step 2: Explanation

As the result from part (c) as:

There is a 90%confident that the genuine mean IQ score of the students will fall somewhere between 111.79and 118.17.

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