Question

Consider the test of Ho σ2-9 against H 1: σ. 9 what are the cntical values for the test statistic XS2 for n= 19 the significance level α=0.05 Order your answers increasingly. Give your answers with two decimal places (e.g. 98.76) A rivet is to be inserted into a hole. A random sample of parts is selected and the hole diameter is measured. The sample standard deviation is S = 0.008 millimeters. Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters? use α- (a) Calculate the test statistic ARound your answer to two decimal places (e.g. 98.76) (b) Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters?

Answer 1

Question 1

Here n = 19 and alpha = 0.05 ,

Degree of freedom dF = 19 - 1 = 18

Here Lower Critical value = X²_0.975,18 = 8.23

Upper Critical value = X²_0.025,18 = 31.53

Question 2

H₀ : σ > 0.01 mm

H_a : σ < 0.01 mm

Here n = 15

alpha = 0.01

Here test statistic

X_o² = (n-1)s²/σ₀² = (15 - 1)*0.008²/0.01² = 8.96

Here critical value of chi - square

X²_critical = X²_0.99,14 = 4.66

so here

X₀² > X²_critical so we failed to reject the null hypothesis and can conclude that there is strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 mm.