Question

The human resources department of a major corporation announced that the number of people interviewed by the corporation in one month has a mean of 108 and a standard deviation, σ, of 15. The management of the corporation suspects that the standard deviation differs from 15. A random sample of 17 months had a mean of 113 interviews, with a standard deviation of 9. If we assume that the number of people interviewed by the corporation in one month follows an approximately normal distribution, is there enough evidence to conclude, at the 0.01 level of significance, that the management's claim is correct?

Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.01 level of significance: (Round to at least three decimal places.) and Can we support the claim that the standard deviation of number of people interviewed by the corporation in one month differs from 15? Yes No

Answer 1

The null hypothesis Ho : = 15

The alternative hypothesis H1 : 15

Test statistic : chi square

Test statistic ² = (n-1)*s^{​​​​​​2}/² = 16*9²/15²

² = 5.760

Critical values for a = 0.01 and d.f = n -1 = 16

  ²critical = ²_{0.005 , 16} = 34.267   and  ²_{0.995 ,16} = 5.142

Critical values are 34.267 , 5.142

Here the chi square test statistic > chi square critical value

We reject null hypothesis

There is sufficient evidence to support the claim that the standard deviation of number of people interviewed by the corporation in one month differs from 15