For each of the following problems, (a) identify the population parameter of interest, (b) define the random variable, and (c) state appropriate null and alternative hypotheses.
1. General Electric has developed a new bulb whose design specifications call for a light output to average 960 lumens. From a sample of 20 new bulbs, the testing committee found a mean light output of 954 lumens. Specify the null and alternative hypotheses General Electric would use to determine whether its new bulb is producing the specified mean light output of 960 lumens?
2. Rick Douglas, the new manager of Food Barn, is interested in the percentage of customers who state, when surveyed, that they are satisfied with the store. The previous manager found that 86 percent of the customers at the time were satisfied. Rick claims the proportion of satisfied customers is the same today. Rick sampled 187 customers and found 157 expressed satisfaction. At the 1 percent level of significance, is there sufficient evidence that refute Rick's claim?
3. From a total of 10,200 loans made by a state employee's credit union in the most recent five year period, 350 were sampled to determine what proportion were made to women. This sample showed that 39 percent of the loans were made to women employees. A complete census of loans 5 years ago showed that 41 percent of borrowers at that time were women. At the 2% level, has the proportion of loans made to women changed significantly in the past 5 years?
4. A television documentary on overeating claimed that Americans are at least 10 pounds overweight on average. To test this claim, eighteen randomly selected individuals were examined; their average excess weight was found to be 12.4 pounds, and the sample standard deviation was 2.7 pounds. At a significance level of 0.01, is there sufficient evidence in the sample data to support the documentary's claim?
5. Federal environmental statutes applying to a particular nuclear power plant specify that recycled water must, on average, be no warmer than 84 degrees F (28.9 C) before it can be released into the river beside the plant. From 70 samples, the average temperature of recycled water was found to be 86.3 F. If the population standard deviation is 13.5 F, should the plant be cited for exceeding the limitation of the statute?
6. Two years ago the average 2-week-advance-purchase airfare between Raleigh-Durham, North Carolina, and New York City was $235. The population standard deviation was $68. A recent sample of 90 randomly chosen travelers between these two cities found that they had paid $218.77, on average, for their tickets. Did the average airfare on this route change significantly in the past two years?