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releasing the reserve parachute at a mean height of 320 0 m with a standard deviation of 12 4 m The company recently updated the devices which the lead engineer suspects has caused the standard deviation G to decrease He measures the heights at which the devices fire for a random sample of 13 of the updated devices The heights at which the devices fire have a sample standard deviation of 9 5 m Assume the heights at which the updated devices fire follow a normal distribution Can the engineer conclude that the population standard deviation o is less than 12 4 m To answer complete the parts below to perform a hypothesis test Use the 0 10 level of significance a State the null hypothesis H and the alternative hypothesis that you would use for the test Ho O O O OSO O 020 Chi square Distribution Step 1 Enter the number of degrees of freedom Step 3 Enter the test statistic Round to 3 decimal places b Perform a chi square test and find the p value Here is some information to help you with your chi square test Step 2 Select one tailed or two tailed O One tailed O Two tailed Step 5 Enter the p value Round to 3 decimal places S X The value of the test statistic is given by The p value is the area under the curve to the left of the value of the test statistic Step 4 Shade the area represented by the p value 0 0 00 03 02 01 10 15 n 1 s 0 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 less than 12 4 m 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 less than 12 4 m c Based on your answer to part b choose what can be concluded at the 0 10 level of significance about the population standard deviation in the heights at which the updated devices fire 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 less than 12 4 m Since the p value is greater than the level of significance the null hypothesis is not rejected 201 30 X 35 S

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