The College Board claims that the average SAT score for the math section of the test is 500 with a standard deviation of 100 points. After interviewing 36 people, it was discovered that their average score was 459. Using 1% significance, does this information indicate that the College Board's statement is inaccurate?

Null hypothesis : The average SAT score for math is NOT equal to 500

Alternate hypothesis : The average SAT score for math is equal to 500

Test statistic = -2.46

The corresponding p-value is = 0.0139

Conclusion :

Here the p-value is greater than the significance level (as 0.0139 > 0.01 ), so the our test results are not significant. Therefore we failed to reject the null hypothesis. So our conclusion will be the null hypothesis. That is "The average SAT score for math is NOT equal to 500"

Which implies , the collage Board's statement is inaccurate

Step-by-step explanation

Calculation of test statistic,

Formula,

Z = (M - μ) / √(σ² / n)

M= Sample mean (459)

?μ? = Population mean (500)

?σ? = population standard deviation (100)

n = sample size (36)

On substitution,

Z = (459 - 500) / √(10000 / 36)

Z = -41 / 16.66667

Z = -2.46

So the value of test statistic = -2.46

The corresponding p-value is = 0.0139 (From standard z-table, available on internet)