math 14
kjjvil
6p.docx6P(304)-
For exercises 5-8 : (a) state the null hypothesis and the alternate hypothesis, (b) state the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.
The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 1 minute. At the Warren Ro ad MacBurger, the quality-assurance department sampled 50 customers and found that mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?
26p(316)-
Research at the University of Toledo indicates that 50% of the students change their major area of study after their first year in a program, A rotation sample of 100 students in the college of Business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the population of students who change their major after the first year in the program? Test at the .05 level of significance.
44p(319)-
For a recent year, the mean fare to fly from charlotte, NC, Seattle, Washinton, on a discount ticket was $370. A random sample of round trip discount fares on this route last month gives:
$421 $366 $390 $430 $410 $350 $370 $380 $380 $399 $365 $391 $375 $381
At the .01 significance level, Can we conclude that the mean fare has increased? What is the p-value?
52p(320)-
Research in the gaming industry showed that 10% of all slot machines in the United States stop working each year. Short’s Game Arcade has 60 slot machines and only 3 failed last year. Use the five step hypothesis-testing procedure at the .05 significance level to test whether this data contradicts the research report.
A- Why can you employ z as the research statistic?
B- State the null and alternate hypothesis.
C- Evaluate the test statistic and make the decision.
D- What is the p-value and what does it imply?
2p(331)-
A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observation is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level
H0:m1<m2
H1:M1>m2
A-Is this a one-tailed or a two-tailed test?
B- State the decision rule.
C- Compute the value of the test statistic.
D-What is your decision regarding H0?
What is the P-value?
6p(332)-
Mary Jo Fitzpatrick is the vice president for Nursing Services at St. Lukes Merorial Hospital. Recently she noticed in the job posting for nurses that those that are unionized seem to offer higher wages. She decided to investigate and gathered the following information.
Group Mean Wage Population Standard Deviation Sample Size
Union $20.75 $2.25 40
nonunion $19.80 $1.90 45
Would it be reasonable for her to conclude that union nurses earn more? Use the .02 significance level. What is the p-value?
12p(336)
The research department at the home office of New Hampshire Insurance conducts ongoing research on the causes of automobile accidents, the characteristics of the drivers, and so on, a random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the .05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three-year period? Determine the p-value.
22p(349)-
The federal Government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high crime areas of Miami, Florida, yielded the following results,
Number of Crimes by Area
A B C D E F G H
Before 14 7 4 5 17 12 8 9
After 2 7 3 6 8 13 3 5
Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the p-value.
48p(355-356)
A goal of literacy for children is to learn how to manage money wisely. One question is How much money do children have? A recent study by Schnur Educational Research Associates revealed the following sample information regarding the monthly allowance that children receive. Is it reasonable to conclude that the mean allowance received by children between 11 and 14 years is more than the allowance received by children between 8 and 10 years? Use the .01 significance level. What is the p-value?
8-10 Tears 11-14 years 8-10 years 11-14 Years
6 19 6 11
13 14 5 8
10 12 7 14
6 8 9 9
14 9 14 20
6 11 12 19
7 9 11
7 8 12
10 8 20
4p(400)-
The production department of celltroicsa International wants to explore the relationship between the number of employees who assembled a subassembly and the number produced. As an experiment, two employees were assigned to assemble them. They produced 25 during a one-hour period. The complete set of paired observation follows.
Location of TV Station Numbers of assemblers One-Hour production (units)
Providence 4 15
Springfeild 2 8
Hew Haven 5 21
Boston 6 24
Hartford 3 17
A- What is the dependent value?
B- Draw a scatter diagram.
C- Determine the correlation coefficient.
D- Interpret these statistical measures.
6p(401)-
The owner of maumee Ford Mercury Volvo wants a study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car Age(years) Selling Price ($000) Car Age(years) Selling Price ($000)
1 9 8.1 7 8 7.6
2 7 6.0 8 11 8.0
3 11 3.6 9 10 8.0
4 12 4.0 10 12 6.0
5 8 5.0 11 6 8.6
6 7 10.0 12 6 8.0
A- Draw a scatter diagram.
B- Determine the correlation coefficient.
C- Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative?
20p(412)-Refer to the chart in yellow.
A- Determine the regression equation
B- Estimate the selling price of a 10 year old car.
C- Interpret the regression equation.
A Suburban hotel derives its gross income from its hotel and restaurant operation. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample 25 days (Mon through Thru.) from last year showing the restaurant income and number of rooms occupied.
Day Income Occupied Day Income Occupied
1 $1452 23 14 $1425 27
2 1361 47 15 1445 34
3 1426 21 16 1439 15
4 1470 39 17 1348 19
5 1456 37 18 1450 38
6 1430 29 19 1431 44
7 1354 23 20 1446 47
8 1442 44 21 1485 43
9 1394 45 22 1404 38
10 1459 16 23 1461 51
11 1399 30 24 1490 61
12 1458 42 25 1426 39
13 1537 54
Sue the statistical software package to answer the following questions.
A- Does the breakfast revenue seem to increase as the number of occupied rooms increase? Draw a scatter diagram to support your conclusion
B- Determine the correlation coefficient between the two variables. Interpret the value.
C- What percent of the variation in revenue in the restaurant as accounted for by the number of rooms.
