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An assembly line has a machine that welds two parts together. When the machine is properly calibrated, its welds have a mean length of 24.00 mm with a standard deviation of 0.27 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, o, of the weld lengths is greater than when this machine is properly calibrated. To do so, you choose at random a sample of size 13 and examine the weld lengths. You find they have a sample standard deviation of 0.32 mm. Assume the weld lengths follow a normal distribution. Is there enough evidence to conclude that the population standard deviation, o, is greater than 0.27 mm? To answer, complete the parts below to perform a hypothesis test. Use the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test.

An assembly line has a machine that welds two parts together. When the machine is properly calibrated, its welds have a mean length of 24.00 mm with a standard deviation of 0.27 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, o, of the weld lengths is greater than when this machine is properly calibrated. To do so, you choose at random a sample of size 13 and examine the weld lengths. You find they have a sample standard deviation of 0.32 mm. Assume the weld lengths follow a normal distribution. Is there enough evidence to conclude that the population standard deviation, o, is greater than 0.27 mm? To answer, complete the parts below to perform a hypothesis test. Use the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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An assembly line has a machine that welds two parts together. When the machine is properly calibrated, its welds have a mean length of 24.00 mm with a standard deviation of 0.27 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, o, of the weld lengths is greater than when this machine is properly calibrated. To do so, you choose at random a sample of size 13 and examine the weld lengths. You find they have a sample standard deviation of 0.32 mm. Assume the weld lengths follow a normal distribution. Is there enough evidence to conclude that the population standard deviation, o, is greater than 0.27 mm? To answer, complete the parts below to perform a hypothesis test. Use the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: O H₁:0 O ロミロ Chi-square Distribution Step 1: Enter the number of degrees of freedom. Step 3: Enter the test statistic. (Round to 3 decimal places.) Step 2: Select one-tailed or two-tailed. O One-tailed O Two-tailed X Step 5: Enter the p-value. (Round to 3 decimal places.) S (b) Perform a chi-square test and find the p-value. Here is some information to help you with your chi-square test. The value of the test statistic is given by x² Step 4: Shade the area represented by the p-value. OSO (n-1)s² 0² • The p-value is the area under the curve to the right of the value of the test statistic. ロ=ロ O<O 0#0 0.3- 0.2 + 0.1 + X (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 weld lengths. O 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 0.27 mm. O 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 0.27 mm. O 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 0.27 mm. O 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 0.27 mm. X
Transcribed Image Text:An assembly line has a machine that welds two parts together. When the machine is properly calibrated, its welds have a mean length of 24.00 mm with a standard deviation of 0.27 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, o, of the weld lengths is greater than when this machine is properly calibrated. To do so, you choose at random a sample of size 13 and examine the weld lengths. You find they have a sample standard deviation of 0.32 mm. Assume the weld lengths follow a normal distribution. Is there enough evidence to conclude that the population standard deviation, o, is greater than 0.27 mm? To answer, complete the parts below to perform a hypothesis test. Use the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: O H₁:0 O ロミロ Chi-square Distribution Step 1: Enter the number of degrees of freedom. Step 3: Enter the test statistic. (Round to 3 decimal places.) Step 2: Select one-tailed or two-tailed. O One-tailed O Two-tailed X Step 5: Enter the p-value. (Round to 3 decimal places.) S (b) Perform a chi-square test and find the p-value. Here is some information to help you with your chi-square test. The value of the test statistic is given by x² Step 4: Shade the area represented by the p-value. OSO (n-1)s² 0² • The p-value is the area under the curve to the right of the value of the test statistic. ロ=ロ O<O 0#0 0.3- 0.2 + 0.1 + X (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 weld lengths. O 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 0.27 mm. O 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 0.27 mm. O 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 0.27 mm. O 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 0.27 mm. X
Over the years, a sushi restaurant has had a mean customer satisfaction rating of 71.2 with a variance of 26.8. The owner wants to see if using a new menu will have any effect on the variance, o². The owner surveys a random sample of 18 customers who ordered from the new menu. For the customers surveyed, the variance of ratings is 45.1. Assume the ratings for customers who order from the new menu follow a normal distribution. Is there enough evidence to conclude that the population variance, o², differs from 26.8? To answer, complete the parts below to perform a hypothesis test. Use the 0.05 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: H₁:0 a ロ<ロ Chi-square Distribution Step 1: Enter the number of degrees of freedom. Step 3: Enter the test statistic. (Round to 3 decimal places.) S 020 0=0 0#0 (b) Perform a chi-square test and find the p-value. Here is some information to help you with your chi-square test. The value of the test statistic is given by ² 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.) OSO (n-1)s² - 0² The p-value is two times the area under the curve to the right of the value of the test statistic. Step 4: Shade the area represented by the p-value. O<O S 0.3 0.2+ 0.1 + 10 20 25 30 35 (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the population variance of ratings for customers who order from the new menu. O 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 variance differs from 26.8. O 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 variance differs from 26.8. O 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 variance differs from 26.8. O 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 variance differs from 26.8. Ś
Transcribed Image Text:Over the years, a sushi restaurant has had a mean customer satisfaction rating of 71.2 with a variance of 26.8. The owner wants to see if using a new menu will have any effect on the variance, o². The owner surveys a random sample of 18 customers who ordered from the new menu. For the customers surveyed, the variance of ratings is 45.1. Assume the ratings for customers who order from the new menu follow a normal distribution. Is there enough evidence to conclude that the population variance, o², differs from 26.8? To answer, complete the parts below to perform a hypothesis test. Use the 0.05 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: H₁:0 a ロ<ロ Chi-square Distribution Step 1: Enter the number of degrees of freedom. Step 3: Enter the test statistic. (Round to 3 decimal places.) S 020 0=0 0#0 (b) Perform a chi-square test and find the p-value. Here is some information to help you with your chi-square test. The value of the test statistic is given by ² 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.) OSO (n-1)s² - 0² The p-value is two times the area under the curve to the right of the value of the test statistic. Step 4: Shade the area represented by the p-value. O<O S 0.3 0.2+ 0.1 + 10 20 25 30 35 (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the population variance of ratings for customers who order from the new menu. O 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 variance differs from 26.8. O 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 variance differs from 26.8. O 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 variance differs from 26.8. O 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 variance differs from 26.8. Ś
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