Question

A retired statistics professor has recorded results for decades. The mean for the score for the population of her students is 82.4 with a standard deviation of 6.5 . In the last year, her standard deviation seems to have changed. She bases this on a random sample of 25 students whose scores had a mean of 80 with a standard deviation of 4.2 . Test the professor's claim that the current standard deviation is different from 6.5 . Use α = .05 .

27) Express the claim in symbolic form.

Express the claim in symbolic form.

Group of answer choices

A )σ > 6.5

B) σ = 6.5

C) σ < 6.5

D) σ ≠ 6.5

E) σ ≥ 6.5

F) σ ≤ 6.5

28) What is the alternative hypothesis, H₁?

Group of answer choices

A) σ < 6.5

B) σ ≤ 6.5

C) σ ≠ 6.5

D) σ = 6.5

E) σ > 6.5

F) σ ≥ 6.5

29) Find the critical value(s). (Round to the nearest thousandth. If more than one value is found, enter the smallest critical value.)

30) Find the value of the test statistic. (Round to the nearest ten-thousandth.)

31) What is the statistical conclusion?

Group of answer choices

A)Fail to reject H₀

B) Reject H₀

₃₂₎ State the conclusion in words.

Group of answer choices

A) There is not sufficient sample evidence to support the claim that the current standard deviation is different from 6.5 .

B) The sample data support the claim that the current standard deviation is different from 6.5 .

C) There is not sufficient evidence to warrant rejection of the claim that the current standard deviation is different from 6.5 .

D) There is sufficient evidence to warrant rejection of the claim that the current standard deviation is different from 6.5 .

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 6.5
Alternative Hypothesis, Ha: σ ≠ 6.5

Rejection Region
This is two tailed test, for α = 0.05 and df = 24
Critical value of Χ^2 are 12.401 and 39.364
Hence reject H0 if Χ^2 < 12.401 or Χ^2 > 39.364
critical value = 12.401

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (25 - 1)*4.2^2/6.5^2
Χ^2 = 10.02

Fail to rej1ct H0

There is not sufficient sample evidence to support the claim that the current standard deviation is different from 6.5 .