# 16. a state education agency designs and administers high school

16. A state education agency designs and administers high school proficiency exams. Historically, time to complete the exam was an average of 120 minutes. Recently the format of the exam changed and the claim has been made that the time to complete the exam has changed. A sample of 50 new exam times yielded an average time of 118 minutes. The standard deviation is assumed to be 5 minutes. Calculate a 99% confidence interval. (Ch 8)

(Points : 10)

[117.61 120.09]

[117.36 119.39]

[116.18 119.82]

[115.67 120.33]

[115.82 120.18]

17. The changing ecology of the swamps in Louisiana has been the subject of much environmental research. One water-quality parameter of concern is the total phosphorous level. Suppose that the EPA makes 15 measurements in one area of the swamp, yielding a mean level of total phosphorus of 12.3 parts per billion (ppb) and a standard deviation of 5.4 ppb. The EPA wants to test whether the data support the conclusion that the mean level is less than 15 ppb. Calculate the appropriate test statistic to test the hypotheses. (Ch 9)

(Points : 10)

7.50

1.94

3.88

-1.94

-7.50

18. If we are testing the significance of the independent variable X1 and we reject the null hypothesis H0: b1=0, we conclude that:(Chs. 13 & 14)

(Points : 10)

X1 is significantly related to Y

X1 is not significantly related to Y

X1 is an unimportant independent variable

b1 is significantly related to the dependent variable Y

19. The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. For premium grade, 14 out of 105 samples failed (they didn’t meet ASTM specification and the FTC Octane posting rule). How many samples would be needed to create a 99% confidence interval that is within 0.02 of the true proportion of premium grade fuel-quality failures?(Ch8)

(Points : 10)

4148

2838

1913

744

54

20. The area under the normal curve between z=2 and z=3 is ________________ the area under the normal curve between z=1 and z=2. (Ch 6) (Points : 10)

Greater than

Less than

Equal to

Answers 1, 2, or 3 depending on the value of the Mean

Answers 1, 2, or 3 depending on the value of the Standard Deviation

21. The least squares regression line minimizes the sum of the (Ch13)

(Points : 10)

Differences between actual and predicted Y values

Absolute deviations between actual and predicted Y values

Absolute deviations between actual and predicted X values

Squared differences between actual and predicted Y values

Squared differences between actual and predicted X values

22. In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99% confidence interval for the true mean length of the bolt? (Ch 8)

(Points : 10)

2.902 to 3.098

2.884 to 3.117

2.871 to 3.129

2.228 to 3.772

2.902 to 3.098

23. If a population distribution is known to be normal, then it follows that: (Ch7) (Points : 10)

The sample Mean must equal the population mean

The sample Mean is skewed for small samples but becomes more and more normal as sample size increases

The sample Standard Deviation must equal the population standard deviation

The Sample Proportion must equal the population Proportion

None of the above

24. If the sampled population has a mean 48 and standard deviation 16, then the mean and the standard deviation for the sampling distribution of X-bar (sample mean) for n=64 are: (Ch7)

(Points : 10)

4 and 4

12 and 4

48 and 2

48 and 1/4

48 and 16

25. A new company is in the process of evaluating its customer service. The company offers two types of sales: 1. Internet sales; 2. Store sales. The marketing research manager believes that the Internet sales are more than 10% higher than store sales. The null hypothesis would be: (Ch 10)

(Points : 10)

Pinternet–Pstore>.10

Pinternet–Pstore[removed]=.10

Pinternet–Pstore <=.10

Pinternet–Pstore=.10

26. A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month. Historical data shows that on the average 18% of the company airplanes have arrived late. In a random sample of 1,240 airplanes, 310 airplanes have arrived late. If we are conducting a hypothesis test of a single proportion to determine if the proportion of late arrivals has increased: What is the value of the calculated test statistic? (Cch 9)

(Points : 10)

Z= 3.208

Z = 6.416

Z= -3.208

Z = -6.416

Z = 1.833

27. A confidence interval increases in width as: (Ch 8)

(Points : 10)

The level of confidence increases

Sample Size n decreases

Sample Standard Deviation increases

All of the above

28. In a manufacturing process, we are interested in measuring the average length of a certain type of bolt. Based on a preliminary sample of 100 bolts, the sample standard deviation is .3 inches. How many bolts should be sampled in order to make us 90% confident that the sample mean bolt length is within .02 inches of the true mean bolt length? (Ch8) (Points : 10)

865

609

1493

100

1000

29. For a given multiple regression model with three independent variables, the value of the adjusted multiple coefficient of determination is _________ less than R2.(Ch 14)

(Points : 10)

Always

Sometimes

Never

Can be greater or less depending on the standard error

30. A manufacturer of a chemical used in glue, attempting to control the amount of a hazardous chemical its workers are exposed to, has given instructions to halt production if the mean amount in the air exceeds 3.0ppm. A random sample of 50 air specimens produced the following statistics: sample mean=3.1 ppm , sample standard deviation=0.5 ppm. Calculate the appropriate test statistic to test the hypotheses. (Ch 9)

(Points : 10)

0.20

-0.20

10.00

1.41

-1.41