Answer:
The value of test statistics is 25.
Step-by-step 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 [tex]\sigma[/tex] = population standard of the reading and writing section SAT score of the students in this school
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \leq[/tex] 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, [tex]H_A[/tex] : [tex]\sigma[/tex] > 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. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2} __n_-_1[/tex]
where, [tex]s^{2}[/tex] = sample variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex] = 13135.8
n = sample of 11th-grade students = 20
So, the test statistics = [tex]\frac{(20-1)\times 13135.8^{2} }{100^{2} }[/tex]
= 24.96 ≈ 25
Hence, the value of test statistics is 25.
