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# solutions7 - ISDS Homework 7 One Sample Hypothesis Testing...

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Unformatted text preview: ISDS Homework 7. One Sample Hypothesis Testing Panayiotis Skordi 1. A production filling operation has a historical standard deviation of 6 ounces. When in perfect adjustment, the mean filling weight for the production process is 50 ounces. A quality control inspector periodically selects at random 36 containers and uses the sample mean filling weight to see if the process is in perfect adjustment. a. State the null and alternative hypotheses. b. Using a standardized test statistic, test the hypothesis at the 5% level of significance if the sample mean filling weight is 48.6 ounces. ANSWER a. 50 : = H 50 : 1 H b. 6 . 48 = X 6 = 36 = n % 5 = Since we have a sample size larger than 30 and we know the population standard deviation we can use the standardized normal methods. Also, since 50 : 1 H we have a two-tailed test. So 96 . 1 % 5 . 2 2 = = Z Z The test statistic is Z, where 4 . 1 36 6 50 6 . 48- =- =- = n X Z H Do NOT reject Ho Reject Ho Reject Ho 1.96 1.96 1.4 z Conclusion: Do not Reject H .We can infer that process is in perfect adjustment. 1 2. A social scientist claims that the average adult watches less than 26 hours of television per week. He collects data on 25 individuals television viewing habits and finds that the mean number of hours that the 25 people spent watching television was 22.4 hours. If the population standard deviation is known to be eight hours, can we conclude at the 1% significance level that he is right? ANSWER a. 26 : H 26 : 1 &amp;lt; H b. 4 . 22 = X 8 = 25 = n % 1 = Although we have a sample size less than 30, we know the population standard deviation and so we can use the standardized normal methods. Also, since 26 : 1 &amp;lt; H we have a one-tailed test with rejection region to the left. So 33 . 2 % 1- = = Z Z The test statistic is Z, where 25 . 2 25 8 26 4 . 22- =- =- = n X Z H Do NOT reject Ho Reject Ho 2.33 2.25 z Conclusion: Do not Reject H .We cant conclude at % 1 = that the social scientist is right. 2 3. A random sample of 100 observations from a normal population whose standard deviation is 50 produced a mean of 75. Does the test statistic provide sufficient evidence at the 5% level of significance to infer that the population mean is not 80?...
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solutions7 - ISDS Homework 7 One Sample Hypothesis Testing...

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