Question

An educational testing service designed an achievement test so that the range in student scores would be greater than 420 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 30 students and found that the sample mean and variance were 759 and 1943, respectively. Assume the range is 6σ. Test whether the test achieved the desired dispersion in scores.

Answer 1

Answer:

Given,

sample size n = 30

6σ = 420

σ = 420/6

standard deviation σ = 70

variance s^2 = 1943

Ho : σ = 70

Ha : σ > 70

let us consider,

alpha = 0.1

degree of freedom = n-1

= 30 - 1

= 29

= 39.087

consider,

test statistic = (n-1)s^2/σ^2

substitute values

= ((30-1)*1943/70^2)

= 11.4994

P value = 0.998464 [since from chi square table]

Here p value > 0.05, so we fail to reject Ho.