Question

Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a standard deviation of

88

minutes. Test the hypothesis that

sigma equals 8σ=8

against the alternative that

sigma less than 8σ<8

if a random sample of the test times of

2323

high school seniors has a standard deviation

s equals 6.18s=6.18.

Use a

0.050.05

level of significance.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 8
Alternative Hypothesis, Ha: σ < 8

Rejection Region
This is left tailed test, for α = 0.05 and df = 22
Critical value of Χ^2 is 12.338
Hence reject H0 if Χ^2 < 12.338

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (23 - 1)*6.18^2/8^2
Χ^2 = 13.129

P-value Approach
P-value = 0.0705
As P-value >= 0.05, fail to reject null hypothesis.

There is no sufficient evidence to conclude that the std. dev. is less than 8