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MATH 302 Quiz 4 Set 4 – Question and Answers

Part 1 of 3

9. A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s production and used them continuously until they failed to work. The life lengths of the batteries, in hours, until they failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, and 298. 
10. The null and alternative hypotheses divide all possibilities into:
11. Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance. 
12. You conduct a hypothesis test and you observe values for the sample mean and sample standard deviation when n = 25 that do not lead to the rejection of H0. You calculate a p-value of 0.0667. What will happen to the p-value if you observe the same sample mean and standard deviation for a sample size larger than 25?
13. In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.
14. In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.
15. The hypothesis that an analyst is trying to prove is called the:
16. A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy? Compute the value of the appropriate test statistic.
17. Which of the following statements are true of the null and alternative hypotheses?
18. If a teacher is trying to prove that a new method of teaching economics is more effective than a traditional one, he/she will conduct a:
19. A type I error occurs when the:

Part 2 of 3

12. A statistician wishes to test the claim that the standard deviation of the weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 30 firemen and found s = 27.2 pounds. Assuming that the weights of firemen are normally distributed if the statistician wanted to test her research hypothesis at the .05 level of significance, what is the critical value? Place your answer, rounded to 3 decimal places, in the blank. For example, 23.456 would be a legitimate entry. 42.558 

13. The ABC battery company claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company’s claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below.
14. The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He believes that the proportion of women in similar sales positions across the country is less than 45%. Hoping to find support for his belief, he directs you to test 
15. A firm that produces light bulbs claims that its lightbulbs last 1500 hours, on average. You wonder if the average might differ from the 1500 hours that the firm claims.  To explore this possibility you take a random sample of n = 25 light bulbs purchased from this firm and record the lifetime (in hours) of each bulb.  You then conduct an appropriate test of the hypothesis. Some of the information related to the hypothesis test is presented below.
16. A survey determines that mint chocolate chip is the favorite ice cream flavor of 6% of consumers. An ice cream shop determines that of 240 customers, 18 customers stated their preference for mint chocolate chip. Find the P-value that would be used to determine if the percentage of customers who prefer mint chocolate chip ice has increased at a 5% level of significance. P-value:  Round your answer to four decimal places as necessary. 

17. Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample of n = 25 light bulbs and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below.

Part 3 of 3

18. Using the confidence interval when conducting a two-tailed test for the population mean, we do not reject the null hypothesis if the hypothesized value for falls between the lower and upper confidence limits.
19. If a null hypothesis about a population proportion p is rejected at the 0.025 level of significance, then it must also be rejected it at the 0.05 level.
20. The probability of making a Type I error and the level of significance are the same.