Name: ___________________________ Unit 5 Test1. Noise levels at urban hospitals are measured in decibels. The mean of the noise levels in a sampleof 45 urban hospitals was 70.9 decibels, with a standard deviation of 6.2 decibels. Find the 95%confidence interval for the true mean noise level for all urban hospitals.
_____________________ ≤ μ ≤ _______________________2. The numbers of advertisements seen or heard in one week for 30 randomly selected people in theUnited States are listed below. Construct a 95% confidence interval for the true mean number ofadvertisements. Assume that σ is 159.5.598 494 441 595 728 690 684481 298 135 846 764 317 649734 588 590 540 673 727 545486 702 703 486 735 808 732582 677a. What is the sample mean for this data?x= ________________b. What is the sample standard deviation for this data? s = _______________c. Find the 98% confidence interval for the population mean commuting distance.
_____________________ ≤ μ ≤ _______________________3. In a random sample of 60 computers, the mean repair cost was $150. Assume the populationstandard deviation is $36. Construct a 90% confidence interval for the population.
_____________________ ≤ μ ≤ _______________________4. In a survey of 300 fatal accidents, 41% showed that they were alcohol related. Construct a 98%confidence interval for the proportion of fatal accidents that were alcohol related.
_____________________ ≤ P ≤ _______________________
5. The standard IQ test has a mean of 104 and a standard deviation of 17. We want to be 98% certainthat we are within 4 IQ points of the true mean. Determine the required sample size.
Sample Size: ______________6. A manufacturer of hand-held calculators receives large shipments of printed circuits from asupplier. It is too costly and time-consuming to inspect all incoming circuits, so when eachshipment arrives, a sample is selected for inspection. Information from the sample is then used totest0 H p: 0.05 versus: 0.05 H p awherepis the true proportion of defective circuits in theshipment. If the null hypothesis is not rejected, the shipment is accepted, and the circuits are usedin the production of calculators. If the null hypothesis is rejected, the entire shipment is returned tothe supplier because of inferior quality.a. In this context, define a Type 1 and Type 2 Error.Type 1:___________________________________________________________________Type 2:___________________________________________________________________b. From the calculator manufacturer’s point of view, which error is considered more seriousand why?
c. From the circuit supplier’s point of view, which error is considered more serious and why?
7. As part of a marketing experiment, a department store regularly mailed discount coupons to 25 ofits credit card holders. Their total credit card purchases over the next three months were comparedto the credit card purchases over the next three months for 25 credit card holders who were notsent discount coupons. Determine whether the samples are dependent or independent.
In questions 8-10, list the null and alternative hypotheses. (Be sure to state which is the claim) Write allpertinent information down (i.e sample size, alpha value, etc). Show your decision based on the decision rulesfor hypothesis testing. (Reject/FTR) Finally, interpret your decision based on the claim.8. A local politician, running for reelection, claims that the mean prison time for car thieves is lessthan the required 4 years. A sample of 80 convicted car thieves was randomly selected, and themean length of prison time was found to be 3.5 years, with a population standard deviation of 1.25years. At α = 0.05, test the politician's claim.: H0 ______________Ha:______________P-value: ______________P α
9. A telephone company claims that 20% of its customers have at least two telephone lines. Thecompany selects a random sample of 500 customers and finds that 88 have two or more telephonelines. If α = 0.05, test the company's claim.: H0 ______________Ha:______________P-value: ______________P α
10. At a local college, 65 female students were randomly selected and it was found that their meanmonthly income was $616 with a population standard deviation of $121.50. Seventy-five malestudents were also randomly selected and their mean monthly income was found to be $658 with apopulation standard deviation of $168.70. Test the claim that male students have a higher monthlyincome than female students. Use α = 0.01.