1. A sample of 40 speedometers of a particular type is selected and each speedometer is calibrated for the accuracy at 55 mph, resulting in a sample mean and sample standard deviation of 53.87 and 1.36, respectively. Does this data suggest that the true average reading when the speed is 55 mph is fact something other than 55? State the relevant hypothesis, calculate the value of the appropriate test statistic, determine p-value, or its range, and state the conclusion for a significance level of 0.01.
2. Plasma-glucose levels are used to determine the presence of diabetics. Suppose the mean ln (plasma-glucose) concentration (mg/dL) in 35-44 age groups is 4.86 with standard deviation of 0.54. A study of 100 sedentary people in the age group is planned to test if they have higher or lower level of plasma glucose than the general population. If the expected difference is 0.10 ln from the mean of the population, for this sample average, is there enough evidence to conclude that there is change in the plasma glucose level.
3. The weight of the cereal in a cereal box is claimed to be 350 grams. If the machine fills more company lose money, and if machine fills less customer will lose money. Is 350 g of the average weight of the contents of the boxes? A simple random sample procedure is followed in selecting the following data.
   348.3 346.1 351.3 352.5 349.4 349.6 349.7 346.8 351.2 349.0 353.7 351.7
   351.1 351.8 352.8 356.0 349.1 347.5 351.9 355.5 351.8 349.5 355.5 348.2
   350.5
4. What is your favorite color? Bunge and Freeman-Gallant from statistic center, Cornell University reported that 24% of the population in several countries indicated that 245 OF the people preferred blue color. Suppose a SRS of 56 students in your campus were surveyed and 12 of them said that they preferred blue color. Does this information imply that the color preference of all the college students is different from the general population?
5. S Mitchell of Sociology department, Ithaca College reported in American Attitude reported that about 28% of the U. S. population believes NAFTA benefits America. In a SRS survey 48 interstate truck drivers showed that 19 believe NAFTA benefits America. Does this indicate that the population proportion of interstate truckers who believe NAFTA benefits America is higher than 28%. What will be your conclusion at 5% and 1% level of significance?
6. Are America’s top chief executive officers (CEO) really worth all that money? One way to answer this question is to look at the percentage of increase in company revenue versus CEO’s annual percentage salary increase in that company. [Forbes Vol. 159, No 10].
   Percent for company 24 23 25 18 6 4 21 37
   Percent for CEO 21 25 20 14 -4 19 15 30
   Do these data indicate that the population means percentage increase in corporate revenue is different from the population mean percentage increase in CEO salary? Use a 5% level of significance.
7. Musculoskeletal neck-and-shoulder disorder is common among office staff who perform repetitive tasks using visual display. The article "Upper-Arm Elevation during Office Work" (Ergonomics, 1996: 1221 1230) reported whether more varied work condition would have impact on arm movement. Each observation is the amount of time, expressed as a proportion of total time observed, during which the arm elevation was below 30°. The two measurements from each subject were obtained 18 months apart.
   Subject: 1 2 3 4 5 6 7 8 9 10
   Before : 81 87 86 82 90 86 90 73 74 75
   After: 78 91 78 78 84 67 92 70 58 72
   Subject: 11 12 13 14 15 16
   Before: 72 80 66 72 56 82
   After: 70 58 66 60 65 73
   How do you check the normality assumption?
   Does the data suggest that the true average time during which elevation is below 30° differ after the change from what it was before the change?
   Does it appear that the change in work conditions decrease true average time by more than 5?
8. A simple random sample of 10 regions in New England states gave the following violent crime rate( per million population)
   x _{1 :} New England crime rate
   3.5 3.7 4.0 3.9 3.3 4.1 1.8 4.8 2.9 3.1
   Another simple random sample of 12 regions in Rocky Mountain states gave the following violent crime rate (per million population)
   x _{2 :} Rocky Mountain States
   3.7 4.3 4.5 5.3 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8
   Assume the data is approximately normal in both regions.
   Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than that in New England? Use 1% level of significance test.
9. Would you favor more federal tax money on the arts? Of a random sample of 93 politically conservative voters 21 responded yes. Another random sample of 83 politically moderate voters 22 responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use α = 0.05.
10. Bases on index harpers Index 37 out of a random sample of 100 adult who did not attend college believe in extraterrestrials. However out of a random sample of 100 adults who did attend college 47 claim that they believe in extraterrestrials. Does this indicate that the proportion of the people who attend college and who believe in extraterrestrials is higher than the proportion who did not attend college? Use α = 0.01.
11. An electrical equipment manufacturer received a shipment of 16,000 circuit boards from a supplier. The company will not accept the shipment if the proportion of defective boards is greater than 3% and management wants to commend the supplier if the proportions of defective boards are less than 3%. Management wants to know if the number of defective boards in the entire shipment of 16,000 is more or less than 3%, but testing all the boards would be prohibitively expensive. Instead, a random sample of boards is tested. From a random sample of 200 boards (out of 16,000), eight boards were defective. What will be your advice to the management: accept or reject the shipment?
12. Nationwide the shares of carbon emission for the year 2000 are transportation, 33%; industry, 30%; residential, 20%; and commercial 17%. A state hazardous materials official wants to see her state is the same. Her study of 300 emission sources finds transportation, 36%; industry, 31%; residential, 17%; and commercial, 16%. At α = 0.05, is the distribution the same as nationwide reported.
13. An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 7.3 lbs/square inch. The valve was tested on 210 engines and the mean pressure was 7.4 lbs/square inch. Assume the standard deviation is known to be 0.5 lbs/square inch. Is there evidence at the 0.05 level that the valve does not perform to the specifications?
14. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. Do these data provide convincing support for the claim that, on average, male drivers exceed the speed limit by more than female teenage drivers?

Male: 1.3, 1.3, 0.9, 2.1, 0.7, 1.3, 3, 1.3, 0.6, 2.1

Female: -0.2, 0.5, 1.1, 0.7, 1.1, 1.2, 0.1, 0.9, 0.5, 0.5

1. From a company report the following data is given. X= advertising share and Y = market share for particular brand.

1. Construct a scatter plot for these data. Can we use linear regression here/
2. Calculate the regression line and use to obtain the predicted market share when the advertising share is 0.9
3. Compute r ² . How would you interpret this value?
4. Calculate 95% confidence interval for the prediction in (b)

16. For the following statistic:

x = tread mill run time; y = 20km ski time.

a.) Determine the regression line equation.

b.) What would you predict ski time to be for a treadmill time is 10 minutes?

c.) Calculate the prediction interval for (b).

d) Perform the test for the regression slope?

17. The following table shows ceremonial ranking and type of pottery shrerd for a random sample of 434 sherds at a location in Sand Canyon Archaeological project Colorado.

Ceremonial Cooking Jar Decorated Jar

Ranking Shreds Shreds

A 86 49\

B 92 53

C 79 75

Do the data support the claim that ranking and pottery type are independent?

18. National Oceanic and Atmospheric Administration Environmental data service give the average daily temperature in July in a town. The temperature is distributed as normal distribution.

Temp [51,59) [59,67) [67, 75] [75,83) [83,91) [91,99)

Percent 2.35% 13.5% 34% 34% 13.5% 2.35

Observed 16 78 212 221 81 12

Use 1% level of significance to test the claim that the average daily temp follows a normal distribution.

19. Political affiliation funding. A random sample of US senators gave the following information on number of federal dollars spent on the federal projects in their home districts. Using 1% level of significance, test the claim that the federal spending level in home districts is independent of party affiliation.

Party <5 billion 5 to 10 Billion > 10 Billion

Republican 12 19 16

Democratic 8 15 22

20. For problem 1 through 5 construct confidence interval from the sample statistic given to estimate the population parameter discussed in them. Can you make a decision about the testing of hypothesis based on the confidence interval constructed here?

21. Do the complete linear regression analysis for the data you have collected in test 1.

22. Collect data for two sample independent T-test or paired T-test from the public domain and test your own hypothesis. For example: I may wish to test the hypothesis "Girls excel in math than boys in ACT test."

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