Calculate the sample mean () and the sample standard deviation. Use the below equation for the sample standard deviation:  Assuming the sample standard deviation (s) is the same as the population standard deviation (σ), what is the 95% interval estimation of the mean of AHS’s reading scores?  Describe what the interval estimation means in Question above.

Several years ago, the Arcadia school system was criticized because the average Arcadia High School graduate could read at only the ninth-grade level.  After this report was made, a special reading program was established to upgrade skills.  The AHS principal wants to know if the reading program worked.  If it has, he will request that an accreditation team visit the school.  If the program has not improved the reading level to at least 10.0 (sophomore level), the administrator would like to avoid the embarrassment of a poor review.  To determine the average reading level of the senior class, we select ten seniors at random.  We assume that reading scores are normally distributed.  The reading scores for the ten seniors are shown in Table 1.

 

Table 1: Reading Scores for Sample High School Seniors

Student

Reading Score

1

13.4

2

12.1

3

11.4

4

10.6

5

10.3

6

10.2

7

9.8

8

9.7

9

9.4

10

8.6

 

  1.  Calculate the sample mean () and the sample standard deviation. Use the below equation for the sample standard deviation:
  1.  Assuming the sample standard deviation (s) is the same as the population standard deviation (σ), what is the 95% interval estimation of the mean of AHS’s reading scores?
  2.  Describe what the interval estimation means in Question above.
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