Do all work in exam book and show all steps. 1. in a random sample

1. In a random sample of 60 computers, the mean repair cost is $150 with a standard deviation of $36. Construct a 99% confidence interval for the population mean.
2. A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed. $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 4.25 $8.00 $3.00. Find the 95% confidence interval for the population mean.
3. A survey of 600 fatal accidents showed that 166 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone.
4. A local politician, running for reelection, claims that the mean prison time for car thieves is less than the required 4 years. A sample of 80 convicted car thieves was randomly selected, and the mean length of prison time was found to be 3.5 years with a standard deviation of 1.25 years at alpha= .05, test the politician’s claim.
5. The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is less than 7 minutes. A random sample of 20 waiting times has a mean of 5.6 minutes with a standard deviation of 2.1 minutes. If mean wait times are normally distributed, test the bus company’s claim at alpha=.01.
6. A local group claims that the police issue at least 60 speeding tickets a day in their area. To prove their point they randomly selected two weeks. Their research yields the numbers of tickets issued for each day. The data are listed below. At alpha= .01, test the group’s claim. 70 48 41 68 69 55 70 57 60 83 32 60 72 58
7. The engineering school at a major university claims that 20% of its graduates are women. In a graduating class of 211 students, 58 were females. Does this suggest that the school is believable? Use alpha =.05.
8. Fifty-five percent of registered voters in a congressional district are registered Democrats. The Republican candidate takes a poll to assess his chances in the race. He polls 1200 potential voters and finds that 621 plan to vote for the Democratic candidate. Does the Republican candidate have a chance to win? Use alpha =.05 (Hint the Republican has a chance to win if the claimed Democratic registration is less than the claim)
9. A local school district claims that the number of school days missed by its teachers due to illness is below the national average of 5. A random sample of 40 teachers provided the data below. At alpha = .05, test the district’s claim.
0 3 6 3 3 5 4 1 3 5 7 3 1 2 3 3 2 4 1 6
2 5 2 8 3 1 2 5 4 1 1 1 2 1 5 7 5 4 9 3

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