Question

if known the TOEFL score, which can be obtained by 20 college students in college
650,730,510,670,480,800,690,530,590,620,710,670,640,780,650,490,800,600,510,700
from these results it is said that women on average get a value for the TOEFL test of more than 600 with an alpha value of 0.05 prove whether the hypothesis is true

Answer 1

H0: <= 600

Ha: > 600

From the sample data,

= X / n = 12820 / 20 = 641

Sample standard deviation S = sqrt [ ( X² - n ² ) / n-1 ]

= 100.10

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 641 - 600) / ( 100.10 / sqrt(20) )

= 1.83

Critical value at 0.05 significance level with 19 df = 1.729

Since test statistics > 1.729 , Reject the null hypothesis.

We have sufficient evidence to support the claim that women on average get a value for the TOEFL test of more than 600