A bolt manufacturer wants to investigate the machine that produces bolts with a diameter of 0.28 centimeters. If the variance of the diameters is equal to 0.025, then the machine is working as expected. A random sample of 11 bolts has a standard deviation of 0.3379. Does the manufacturer have evidence at the α=0.005 Assume the population is normally distributed. step 1: state the null and alternate hypothesis. step 2:determine the critical value of the test statistic. separate 2 tailed with comma. step 3: determine the value of the test statistic. step 4: make decision: reject the null hypothesis or fail to reject null hypothesis step 5: what is the conclusion? there IS sufficient evidence to show the variance of the bolt diameters is more than required. or there is NOT sufficient evidence to show the variance of the bolt diameters is more than required
H0: sigma = 0.025
Ha: sigma > 0.025
s = 0.3379
n = 11
df = 10, critical value is 25.1882
Test statistic,
chi-square = (n-1)*(s/sigma)^2
= 10 * 0.3379^2/0.025
= 45.6706
reject the null hypothesis
there is sufficient evidence to show the variance of the bolt diameters is more than required
A bolt manufacturer wants to investigate the machine that produces bolts with a diameter of 0.28...
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