Question

Use a α=0.05 significance level to test the claim that σ=19 if the sample statistics include ,n=10 ,x¯=93, and s=26.
The test statistic is
The smaller critical number is
The bigger critical number is
What is your conclusion?

A. There is not sufficient evidence to warrant the rejection of the claim that the population standard deviation is equal to 19
B. There is sufficient evidence to warrant the rejection of the claim that the population standard deviation is equal to 19

Answer 1

Answer:

Given,

sample size n = 10

mean x¯= 93 and

Standard deviation s = 26

σ = 19

Null hypothesis Ho : σ = 19

Alternative hypothesis Ha : σ != 19

consider,

Test statistics

= (n -1) S² / σ^2

substitute values

= (10 - 1)*26^2 / 19^2

= 16.85

degree of freedom = n - 1

= 10 - 1

= 9

Smaller critical number = 2.7

The bigger critical number is 19.023 [since from chi square calculator]

Here we observe that 16.85 < 19.023 , so we fail to reject Ho at 0.05 level

So there is not sufficient evidence to warrant the rejection of the claim that the population standard deviation is equal to 19