Name: __________________________ Date:
Name: __________________________ Date: _____________
|1. |A manufacturer claims that his television will have an average lifetime of at least five years. The standard deviation is seven |
| |months. 81 televisions are selected at random, and their average lifetime was found to be 59 months. Is the manufacturer |
| |correct? Use [pic] . |
|2. |Science fiction novels average 300 pages in length. The average length of 12 randomly chosen novels written by I. M. Wordy was |
| |330 pages in length with a standard deviation of 55. Are Wordy's novels significantly longer than the average? Assume [pic] = |
| |.05. |
|3. |Dr. Christina Cuttleman, a nutritionist, claims that the average number of calories in a serving of popcorn is 75 with a |
| |standard deviation of 7. A sample of 50 servings of popcorn yields an average of 78 calories. Check Dr. Cuttleman's claim at |
| |[pic] . |
|4. |A random sample of 450 shoppers at Quincy Mall found that 150 favored longer shopping hours. Is this sufficient evidence to |
| |conclude that less than 30% of the shoppers at Quincy Mall favor longer hours? Let [pic] |
|5. |Reginald Brown, an inspector from the Department of Weights and Measures, weighs 15 eighteen-ounce cereal boxes of corn flakes. |
| |He finds their mean weight to be 17.78 ounces with a standard deviation of 0.4 ounces. Are the cereal boxes lighter than they |
| |should be? Let [pic] . |
|6. |It has been claimed that at U.C.L.A. at least 40% of the students live on campus. From a sample of 250 students, 90 live on |
| |campus. Does the evidence support this claim at [pic] ? |
|7. |Assume that a 95% confidence interval for the mean is (13.0, 15.0). What is the result of a hypothesis test of [pic] = 12.0 at |
| |[pic] 0.05? |
|8. |Are the following statements |
| |[pic]: [pic] [pic] 5 |
| |[pic]: [pic][pic] 17 |
| |a valid pair of null and alternative hypothesis? |
|9. |Is the statement |
| |[pic]: 13 = 11 |
| |a valid null hypothesis? |
|10. |Using the z-table, find the critical value (or values) for a [pic]= .07 two-tailed test. |
|11. |If the observed value is 8, the expected value is 5, and the standard error is 2, then the test value used for the z test is |
| |equal to what? |
|12. |Is the statement |
| |[pic]: = 6 |
| |a valid null hypothesis? |
|13. |In a particular city, the average salary of secretaries is $30000 per year. Secretaries at Company A claim that they are paid |
| |less than the city average. In a sample of 45 secretaries, their average salary was $25000 per year with a standard deviation of|
| |$5000. What is the test value for this hypothesis? |
|14. |If the observed value is 7, the expected value is 8, and the standard error is 2, then the test value used for the z test is |
| |equal to what? |
|15. |A lumber mill is tested for consistency by measuring the variance of board thicknesses. The target accuracy a variance of |
| |0.0015 or less. If 24 measurements are taken and their variance is 0.005, is there enough evidence to reject the claim that her|
| |standard deviation is within the limit at [pic] = .01? |
|16. |For the conjecture "The average rent of an apartment is more than $750 per month", what is the alternative hypothesis? |
|17. |Nationwide, the average waiting time until a electric utility customer service representative answers a call is 300 seconds per |
| |call. The Gigantic Kilowatt Energy Company took a sample of 50 calls and found that, on the average, they answered in 280 |
| |seconds per call with a standard deviation of $55. Can the company claim that they are faster than the average utility? |
|18. |Using the z-table (Table E), find the critical value (or values) for a [pic]= .11 right-tailed test. |
|19. |Are the following statements |
| |[pic]: [pic]12 |
| |[pic]: [pic] 12 |
| |a valid pair of null and alternative hypothesis? |
|20. |An average computer mouse inspector can inspect 45 mice per hour. The 42 computer mice inspectors at a particular factory can |
| |only inspect 40 mice per hour with a standard deviation of 8. Does the company have reason to believe that these inspectors are|
| |slower than average? |
Answer Key
|1. |[pic] Do not reject [pic] . It appears that the manufacturer's claim is correct and his television will have an average |
| |lifetime of at least five years. |
|2. |The test value is 1.89 and the critical values are [pic] 2.201, so the conclusion is to not reject the null hypothesis. |
|3. | [pic] Reject [pic]. It appears that the average number of calories of popcorn is not 75. |
|4. |[pic] |
| |Critical Value: 1.65 |
| |[pic] |
| |Do not reject [pic]. The evidence is not sufficient to support the claim that less than 30% of the shoppers favor longer hours.|
|5. |[pic] Do not reject [pic] because –2.13 does not fall within the critical region. There is not enough evidence to support Dr. |
| |Brown's claim that the cereal boxes are lighter than they should be. |
|6. |[pic] Critical Value: -2.33 [pic]Do not reject [pic]. The claim that at least 40% of the students at U.C.L.A. live on campus |
| |is supported by the evidence. |
|7. |Rejecting the null hypothesis because 12.0 is less than 13.0 |
|8. |No, these statements have overlapping regions |
|9. |No, there is no parameter contained in this statement |
|10. |[pic]1.8119 |
|11. |1.50 |
|12. |No, there is no parameter contained in this statement |
|13. |–6.71 |
|14. |–0.50 |
|15. |Yes, comparing the test value 76.67 and the critical value 41.64. |
|16. |The average rent of an apartment is less than or equal to $750 per month" |
|17. |Yes, because –2.57 falls in the critical region |
|18. |1.5982 |
|19. |Yes, these statements have two non-overlapping hypotheses and compare a parameter to a value |
|20. |Yes, because –4.05 falls in the critical region |
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