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machine is properly calibrated its welds have a mean length of 22 00 mm with a standard deviation of 0 16 mm It has been a while since the machine has been serviced Because of this the foreman has told you to perform a hypothesis test to determine if the standard deviation G of the weld lengths is greater than when this machine is properly calibrated To do so you choose at random a sample of size 11 and examine the weld lengths You find they have a sample standard deviation of 0 21 mm Assume the weld lengths follow a normal distribution Is there enough evidence to conclude that the population standard deviation o is greater than 0 16 mm To answer complete the parts below to perform a hypothesis test Use the 0 05 level of significance a State the null hypothesis H and the alternative hypothesis H that you would use for the test Ho O O O O 0 0 0 0 020 O O OSO b Perform a chi square test and find the p value Here is some information to help you with your chi square test Chi square Distribution Step 1 Enter the number of degrees of freedom Step 3 Enter the test statistic Round to 3 decimal places The value of the test statistic is given by n 1 s G S The p value is the area under the curve to the right of the value of the test statistic Step 2 Select one talled or two tailed O One tailed OTwo tailed Step 5 Enter the p value Round to 3 decimal places X Step 4 Shade the area represented by the p value 03 624 0 1 10 c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the population standard deviation in the weld lengths Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the standard deviation is greater than 0 16 mm Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the standard deviation is greater than 0 16 mm 20 Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the standard deviation is greater than 0 16 mm Since the p value is greater than the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the standard deviation is greater than 0 16 mm 30 X 14

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