Cost of meals: A sample of eight dishes for a new restaurent's menu was created, and the cost of each meal (dish), in dollars is: 30 35 19 23 27 22 26 16 a) Are the assumptions for constructing a confidence interval for the mean satisfied? Explain. b) If appropriate, construct a 98% confidence interval for the mean cost of a repair.
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Cost of meals: A sample of eight dishes for a new restaurent's menu was created, and the cost of each meal (dish), in dollars is:
30
35
19
23
27
22
26
16
a) Are the assumptions for constructing a confidence interval for the
b) If appropriate, construct a 98% confidence interval for the mean cost of a repair.
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- What is meant by the sample space of an experiment?Using p-value approach or using the confidence interval Average college cost of tuition fee for all private institutions last year was P36, 400. A random sample of costs this year for 45 institutions of higher learning indicated that the sample mean was P37,900 and a sample standard deviation was P5,600. At the 0.10 level of significance, is there sufficient evidence to conclude that the cost has increased? (Illustrate the six (6) steps in hypothesis testing using the p-value approach or the confidence interval.)Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. The article “Postoperative Complications in Patients With Obstructive Sleep Apnea Syndrome Undergoing Hip or Knee Replacement: A Case-Control Study” (R. Gupta, J. Parvizi, et al., Mayo Clinic Proceedings, 2001:897–905) reported that in a sample of 427 people 65 and over, 104 of them had sleep apnea. a) Find a 95% confidence interval for the proportion of those 65 and over who have sleep apnea. b) Find a 99% confidence interval for the proportion of those 65 and over who have sleep apnea. c) Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.03. d) Find the sample size needed for a 99% confidence interval to specify the proportion to within ±0.03.
- Seat Belt ProblemA random sample of car crashes is obtained. Among 2792 occupants not wearing seat belts, 33 were killed. Among 7654 occupants wearing seat belts, 18 were killed. Use a 0.01 significance level to test the claim that seat belts are effective in reducing fatalities. Consider the occupants not wearing seat belts to be population 1. Test the claim by constructing a 98% confidence interval.Round values to 3 decimal places. ___________ < (p1 - p2) < ___________Crash testing is a highly expensive procedure to evaluate the ability of an automobile to withstand a serious accident. A simple random sample of 12 small cars were subjected to a head-on collision at 40 miles per hour. Of them 8 were “totaled,” meaning that the cost of repairs is greater than the value of the car. Another sample of 15 large cars were subjected to the same test, and 5 of them were totaled. Find a 95% confidence interval for the difference in the proportions of small cars and large cars that are totaled.Race and smoking 2010 Data collected in 2010 by theBehavioral Risk Factor Surveillance System revealedthat in the state of New Jersey, 15.7% of whites and15.9% of blacks were cigarette smokers. Suppose theseproportions were based on samples of 2449 whites and464 blacks.a) Create a 90% confidence interval for the difference inthe percentage of smokers between black and whiteadults in New Jersey.b) Does this survey indicate a race-based difference insmoking among New Jersey adults? Explain, using yourconfidence interval to test an appropriate hypothesis.c) What alpha level did your test use?
- Pottery Archaeologists can use the chemical composi-tion of clay found in pottery artifacts to determine whether different sites were populated by the sameancient people. They collected five samples of Romano–British pottery from each of two sites in Great Britainand measured the percentage of aluminum oxide in each.Based on these data, do you think the same people usedthese two kiln sites? Base your conclusion on a 95%confidence interval for the difference in aluminum oxidecontent of pottery made at the sites. (A. Tubb, A. J. Parker,and G. Nickless, “The Analysis of Romano–BritishPottery by Atomic Absorption Spectrophotometry.”Archaeometry, 22[1980]:153–171) Ashley Rails 19.1 14.8 16.7 18.3 17.7New Forest 20.8 18.0 18.0 15.8 18.3In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1=not attractive; 10=extremely attractive). Construct a confidence interval using a 90% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females? 5,7,2,9,4,4,6,9,7,8,6,8in a study of cell phone use and brain hemispheric dominance, an internet survey was e-mailed to 2457 subjects randomly selected from an online group involved with ears. 1071 surveys were returned. construct a 95% confidence interval for the proportion of returned surveys. a) find the best point estimate of the population proportion p.