Question

Experience indicates that the time required for the college of engineering students to complete a final exam of BE 2100 is a normal random variable with a standard deviation of at most 8 minutes. Test the claim if a random sample of the test times of 18 high school seniors has a standard deviation of 81. Use a 0.05 level of significance.level?

Answer 1

Here, we have to use Chi square test for the population variance or standard deviation.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: The population standard deviation is at most 8 minutes.

Alternative hypothesis: H_a: The population standard deviation is greater than 8 minutes.

H₀: σ ≤ 8 versus H_a: σ > 8

This is an upper tailed test.

The test statistic formula is given as below:

Chi-square = (n – 1)*S^2/ σ²

From given data, we have

n = 18

S = 81

σ² = 8^2 = 64

Chi-square =(18 - 1)*81^2/64

Chi-square = 1742.7656

We are given

Level of significance = α = 0.05

df = n – 1

df =17

Critical value = 27.5871

(by using Chi square table or excel)

P-value = 0.0000

(by using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the variable is the normal random variable with a standard deviation of at most 8 minutes.