2) The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in an area and finds 380 in which a firearm was reportedly used Find a 99% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used. 3) Sales of a new line of athletic footwear are crucial to the success of a company. The company wishes to estimate the average weekly sales of the new footwear to within $300 with 90% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately$1100. How many weeks of data must be sampled for the company to get the information it desires? 4) State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 760 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 760 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the 01 significance level. Suppose 92 bulbs were tested with the following results: Mean = 778 hours and standard deviation 91 hours. Use the data to conduct a test of hypotheses.

Question

The scores on a standardized test are reported by the testing agency to have a mean of 70. Based on his personal observations, a school guidance counselor believes the mean score is much higher. He collects the following scores from a sample of 50 randomly chosen students who took the test.

39     48     55     63     66     68     68     69     70     71

71     71     73     74     76     76     76     77     78     79

79     79     79     80     80     82     83     83     83     85

85     86     86     88     88     88     88     89     89     89

90     91     92     92     93     95     96     97     97     99

Use the data to conduct a test of hypotheses at α = .05 to determine whether there is any evidence to support the counselor's suspicions.