Hypothesis Testing II

Transcription

1 Hypothesis Testing II Tests for the Proportion and the Difference Between Two Means WEEK NINE This worksheet relates to parts of chapter eight and nine of the text book (Statistics for Managers 4 th Edition). Remember to try hypothesis testing on the computer. In your exam you will more than likely be asked to interpret PHStat output. This is a lot easier if you ve spent time working with PHStat. RELEVANT QUESTIONS FOR HYPOTHESIS TESTING Is the test one-tail or two-tail? Look for key words or phrases: Two Tail Different The same as Equal to No difference One Tail Greater than No Larger than Exceeds Increases Is the standard deviation of the population(s) known? Yes - Use the Z-Distribution No Use the t-distribution Are there one or two samples? If there are two samples, are they independent or dependent? If they are independent, use the Z-Distribution if the population standard deviations are known, or use the t-distribution and calculate the pooled variance if the population standard deviations are unknown. 65

2 CALUCLATION QUESTIONS 1. Refer back to the calculation question done last week. A manufacturer of chocolate topping uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses toppings is working properly when 8 grams are dispensed. The standard deviation of the process is 0.15 gram. A sample of 50 bottles is selected periodically and the filling line is stopped if there is evidence that the average amount dispensed is actually less than 8 grams. Suppose that the average amount dispensed in a particular sample of 50 bottles is grams. At the 0.05 level of significance, is there evidence that the average amount dispensed is less than 8 grams? Complete this question again but use the p-value approach. Compare the conclusions of each approach. What do you find? 66

3 2. An article in the Wall Street Journal implies that more than half of all Americans would prefer to be given $100 than a day off work. This statement is based on a survey conducted by American Express incentive Services, in which 593 of 1040 respondents indicated that they would rather have the $100. At the 0.05 level of significance, based on the survey data, do you find evidence that more than half of all Americans would rather have $100 than a day off work? 67

4 3. The operations manager at a chocolate factory wants to determine if there is any difference in the average chocolate content of chocolate bars manufactured using 2 different machines. The process standard deviation of machine A is 110 grams and machine B has a standard deviation of 125 grams. A random sample of 27 chocolate bars obtained from machine A indicates a sample mean of 375 grams, and a similar sample of 30 from machine B indicates a sample mean of 362 grams. Using 0.05 level of significance, is there any evidence of a difference in the average chocolate content of chocolate bars produced by the 2 machines? 68

5 4. An inner city real estate agency wants to compare the appraised values of apartments north and south of the CBD. A sample of 60 listings north and 99 listings south of the CBD yields the following results (in thousands of dollars): North South X S n At the 0.05 level of significance is there evidence of a difference in the average appraised values for apartments north and south of the CBD? 69

6 MULTIPLE CHOICE PRACTICE 1. When testing the hypotheses H 0 : p 0.6 H 1 : p<0.6, a sample of 40 gave a sample proportion of The standard error is calculated to be (a) (b) (c) (d) 9.9 Final Exam, June A hypothesis test has been carried out with the following results from Ph Stat Lower Critical Value Upper Critical Value p-value (a) the null hypothesis would be rejected if α was specified at 5% (b) the alternative hypothesis will be accepted if α was specified at 5% (c) there is a 29% chance that the null hypothesis will be rejected (d) the null hypothesis would not be rejected if α was specified at 10% 3. If the p-value is less than α in a two tail test (a) (b) (c) (d) the null should not be rejected the null should be rejected a one-tail test should be used α should be changed 70

7 4. Let p be the value for a given upper tail hypothesis test, α be the significance level, t crit be the critical value for the test, and t calc be the calculated test statistic. You will not reject the null if (a) (b) (c) (d) p > α p < α t calc > t crit (b) and (c) but not (a) 71

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