Question

SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school are given below. 380 520 480 510 560 630 670 490 500 550 400 350 440 490 620 660 700 730 740 560 Test if the standard deviation of the reading and writing section SAT score of the students in this school is higher than 100. What is the value of the test statistic (round off to the nearest integer)

Answer 1

The value of test statistics is 25.

Explanation:

We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;

380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560

Let
`\sigma` = population standard of the reading and writing section SAT score of the students in this school

So, Null Hypothesis,
`H_0` :
`\sigma \leq` 100 {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}

Alternate Hypothesis,
`H_A` :
`\sigma` > 100 {means that the reading and writing section SAT score of the students in this school is higher than 100}

The test statistics that would be used here is One-sample Chi-square test statistics;

T.S. =
`((n-1)s^(2) )/(\sigma^(2) )` ~
`\chi^(2) __n_-_1`

where,
`s^(2)` = sample variance =
`(\sum (X-\bar X)^(2) )/(n-1)` = 13135.8

n = sample of 11th-grade students = 20

So, the test statistics =
`((20-1)* 13135.8^(2) )/(100^(2) )`

= 24.96 ≈ 25

Hence, the value of test statistics is 25.