# HW9sol - IE 300/GE 331 Homework 9 Solutions 9-80 Data from...

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IE 300/GE 331 Homework 9 Solutions 1 9-80 Data from an Izod impact test was described in Exercise 8-28. The sample standard deviation was 0.25 and n=20 specimens were tested. (a) Test the hypothesis that ± ²³´² against an alternative specifying that µ ²³´² , using ¶ ± ²³²´ , and draw a conclusion. State any necessary assumptions about underlying distribution of the data. (b) What is the P-value for this test? (c) Could the question in part (a) have been answered by constructing a 99% two-sided confidence interval for · (a) In order to use the ¸ · statistic in hypothesis testing and confidence interval construction, we need to assume that the underlying distribution is normal. (1) The parameter of interest is the true standard deviation of Izod impact strength, . However, the answer can be found by performing a hypothesis test on · (2) ¹ º »¼½ · ± ¾²³´²¿ · (3) ¹ º »¼½ · µ ¾²³´²¿ · (4) À ± ²³²´ (5) Á º · ± ¾ÂÃÄ¿Å Æ Ç Æ (6) Reject ¹ º if Á ² È É Á ´Ê À È ËÌÊ´ È or Á ² È Í Á À È ËÌÊ´ È where Á ²³ÎÎÏË´Î È ± Ð³ÑÒ and Á ²³²²ÏË´Î È =38.58 (7) n=20,s=0.25, ¼Á º · ± ¾ÂÃÄ¿Å Æ Ç Æ ± ÄÓ¾º³·Ô¿ Æ º³Ä Æ =118.75 (8) Since 118.75>38.58, we reject ¹ º and conclude that there is sufficient evidence to indicate that the true standard deviation of Izod impact strength is significantly different from 0.10 at À ± ²³²´ (b) P-value<0.005 (c) 99% confidence interval for ½ · » For

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HW9sol - IE 300/GE 331 Homework 9 Solutions 9-80 Data from...

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