Standard Deviation and Shape of The Distribution Answer

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Standard Deviation and Shape of The Distribution Answer

I have this 53 math statistic questions and I need to answer it.

Please make sure you can do it correct I must get at least 90% correct.

The yearly average price of unleaded regular gasoline fluctuated as follows:

Year Price per gallon

1983 $1.24

1993 $1.11

2003 $1.59

2012 $3.59

1.What is the gasoline price index number (1993=100) for the year 2012?

A. 143.2

B. 323.4

C. 359.0

D. cannot be determined

  • If the Consumer Price Index (1982 — 84 = 100) is 152.9, this means

A. taking 1984 = 100, the current price is 1984/152.9 = $12.98.

B. prices have increased 152.9%, so it now costs $252.90 to buy goods and services that cost $100 in 1984.

C. prices have increased 52.9%, so it now costs $152.90 to buy goods and services that cost $100 to in 1984.

D. a mistake has been made, because an index number can only take values between 0 and 100.

  • When Julie started college in 1990, she set a goal of making $30,000 when she graduated. The CPI in 1990 was 130.7. Julie graduated in 1995 when the CPI was 152.9. What must Julie earn in 1995 to have the same buying power that $30,000 had in 1990?

A. About $39,200

B. About $35,100

C. About $45,900

D. About $25,600

4. From these choices, which is the best graphical method for displaying the distribution of countries Olympic gold medalists come from?

A. histogram

B. line graph

C. bar graph

D. boxplot

E. stemplot

  • What is the direction, form, and strength of the relationship between x and y shown in this scatterplot?
  • negative, straight-line, weak
  • negative, straight-line, strong
  • negative, curved-line, strong
  • negative, curved-line, weak
  • positive, curved-line, strong
  • positive, straight-line, weak
  • positive, straight-line, strong
  • positive, curved-line, weak |
  • What is the best estimate of the correlation ® shown in this scatterplot?
  • What is the mean return during this period?
  • -0.8
  • -0.2
  • 0
  • 0.3
  • 0.7

Use this information to answer the next eight questions.

The stock market did well during the 1990s. Here are the percent total return(chance in price plus dividends paid) for the Standard & Poor’s 500 stock index:

Year 1989 1990 1991 1992 199319941995199619971998

Return 31.7 -3.1 30.57.610.11.337.623.033.428.6

A. 5.7

B. 20.0

C. 25.8

D. 28.6

E. 23.0

8. What is the third quartile of these returns?

A. 31.2

B. 31.7

C. 30.5

D. 33.4

E.7.6

8.What is the mean return?

A.20.70

B.33.40

C.20.07

D.22.30

E.25.80

10. Suppose that the correlation of US stock returns with overseas stock returns during these years was r= 0.44, What does this tell you?

A. When US stocks rose, Overseas stocks also tended to rise, but the connection was not very strong.

B. When US stocks rose, overseas stocks tended to fall, but the connection was not very strong.

C. When US stocks rose, overseas stocks rose by nearly the same amount

D. There is almost no relationship between changes in US stocks andthe changes in overseas stocks.

E.Nothing, because this is not a possible value of r

11. If x is the return on US stocks (for example, x =5 means 5% return ) and Y is the return on overseas stocks in the same year, the least-square regression line for predicting Y from Xis y-hat = -2.7 + 0.47x. The US stocks had a return of 10.1% in the year 1993.Using this regression line, you predict that the return on overseas stock that years was

A. 2.05%.

B. -2:23%

C. 3.17%.

D. 27.23

12. Refereeing to the regression line in the previous question, how would you interpret the slop 0.47?

  • There is not change in the return on overseas stock when the returnon US stock is 0.47%
  • The return on overseas stock increases by 0.47%, on average, when the retutn on US stocks increases by 1 percent
  • The return on overseas stock increases by 0.47%,on average, when the return on US stock is equal to zero
  • The return on US stocks increases by 0.47% on average, when the return on overseas stocks increase by 1 percent.

13.As indicated previously, the correlation of US stock return with overseas stock returns during these years was r= 0.44. What percent of the variation in overseas stock returns (y) can be explained by the least-squares regression line presented previously?

A. 0.194%

B. 0.440%

C. 44.0%

D. 19.4%

  • You have similar data for returns on US Stocks for all years since 1945. To clearly show how returns have changed over time, what is your best choice of graph?

A. Histogram

  • Line graph
  • Bar graph
  • Boxplot
  • Pie chart
  • The five-number summary of the distribution of scores on a midterm psychology exam is 58, 74, 86, 92, 100. With only this information, which of the following graph could you draw?
  • The five-number summary of the distribution of scores on a midterm psychology exam is 58, 74, 86, 92, 100. Approximately what percent of the exam scores in the previous question are between 58 and 92?

A. scatterplot

B. boxplot

C. both a histogram and a boxplot

D. histogram

A.95%

  • 25%
  • 50%
  • 68%
  • 75%
  • To display the distribution of the lengths in centimeters of a sample of brook trout’s, what graph should you use?

A. line graph

B. scatterplot

C. pie chart

D._ bar chart

E. histogram

  • Which of the following statements is not true of the standard deviation, s, of the length in the centimeter of a sample of brook trout?
  • If the lengths of the trout vary, then s must be greater than 0.
  • S would increase if we included an unusually short trout in our sample.
  • The unit of measurement for s in centimeters
  • S would not change if we measured these trout in inches instead of centimeters.

19. Which of the following statement is not true of the correlation, r, between the lengths in centimeters and weight in pound of a sample of brook trout?

A. r must take a value between —1 and 1.

B. r would not change if we measured these trout in inches instead of centimeters.

C. r is measured in centimeters per pound.

D. If longer trout tend to also be heavier, then r is greater than 0.

  • George has an average bowling score of 180 and bowls in a league where the averagefor all bowlers is 150 and the standard deviation is 20. Bill has an average bowling sore of 190 and bowls in a league where the average is 160 and the standard deviation is 15.Who ranks higher in his own league, George or Bill?

A. Bill, because his score of 190 is higher than George’s 180.

B. Bill, because his standard score is higher than George’s.

C. Bill and George have the same rank in their leagues, because both are 30 pins above the mean.

D. George, because his standard score is higher than Bill’s.

  • Luke’s score is at the 85th percentile of the distribution of SAT scores. This means that
  • Luke answered 85% of the questions correctly.
  • Luke answered 85% of the questions incorrectly.
  • Luke’s score was equal to or higher than approximately 85% exam of the people who took this exam
  • Luke’s score was equal to or lower than approximately 85% of the people who took this exam.
  • There is a positive correlation between the size of a hospital; ( measured by the number of beds) and the median number of days that patients remain in the hospital.Does this means that you can shorten a hospital stay by choosing to go to a smaller hospital?

A.No. A negative correlation would allow that conclusion, but this correlation in positive.

B.Yes. Strong correlation proves causation.

C.Yes. The data show that stays are shorter in smaller hospitals.

  • No. The positive correlation is probably explained by the fact that serious ill people go to large hospitals.

23. Mary standards score on a SAT is -3. Which is the following is the best explanation of Mary’s standards score?

  • Mary missed three question on the SAT.
  • Of those taking the SAT, 3% scored lower than Mary
  • Of those taking the SAT, 3% scored higher than Mary
  • Mary’s SAT score is 3 standard deviations below the average SAT score.
  • Mary SAT score is three times below the average SAT score.
  • Mary’s SAT score is 3 point below the average SAT score.

Use this information to answer the next five questions.

The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. The figure below is the normal curve for this distribution of the length of human pregnancies measured in days, where linesdelineate standards deviations from the mean.

Use the 68-95-99.7 rule or Table B to answer the questions.

  • Point T corresponds to
  • What range covers the middle 95% of lengths of human pregnancies?

A. 234 days

B. 202 days

C. µ+3ᶞ

D. 218 days

A. 234 to 298 days

B. 218 to 314 days

C. 250 to 282 days

D. 218 to 282 days

26. What percent of human pregnancies are longer than 250 days?

A. 16%

B. 34%

C. 68&

D. 84%

27. What percent of human pregnancies are between 234 and 282 days?

A. 68.0

B. 81.5%

C. 84.0

D.99 .7%

28. Approximately 24% of the human pregnancies are shorter than_____ days

A.260

B. 255

C. 250

D. 234

  • This graph shows the estimates for religious adherents in the Salt Lake metropolis in 2010 based on the US Religion Census of 2010. The counts listed are in thousands.

Approximately what percentage of the 1,029,655 Salt Lake metropolis residents in 2010 were not unclaimed?

A. 0.27%

B. 27%

C. 60%

D. 73%

  • In general, the standard deviation can bedescribed as
  • An indicator of where the data tend to cluster
  • The distance between the smallest and largest observations
  • The average distance of observation from their mean.
  • An indicator of the shape of the distribution
  • The maximum distance from one observation to the next.

31. The statistics student collected data for a term project and found the mean of his data to be 20 and the standard deviation to be 2. Later he discovered that one of his observations had accidentally been recorded as I9 and should be recorded as 19. What will happen to his mean and standard deviation once he fixes the recording error?

  • The mean will stay the same and the standard deviation will increase
  • The mean will increase and the standard deviation will decrease
  • The mean will decrease and the standard deviation will increase
  • The mean will increase and the standard deviation will increase.
  • The mean will decrease and the standard deviation will decrease.

32. Which statistical measure is not strongly affected by a few outliers in the data?

A. The mean

B.The correlation coefficient

C.The standard deviation

D.The median

33. Adult women in China have heights which are normally distributed with the mean of 155 centimeters and a standard deviation of 8 centimeters. Adult women in Japan have heights which are normally distributed with mean 158 centimeters and standard deviation 6 centimeters. Which country has the higher percentage of women taller than 167 centimeters?

  • China
  • the percentage are approximately the same
  • Japan
  • It is not possible to tell from the information given

Use this information to answer the next three questions

This is a histogram of milligrams of potassium in 80 selected cereals.

Milligrams of Potassium in 80 Cereals

  • Which one of the following values is the best estimate of the median for this distribution?

A. 20

B. 90

C. 125

D.175

  • Why does the histogram represent a distribution?

A. Because the range of possible potassium content is from 15 to 335 milligrams

B. Because values for potassium content are given on the horizontal axis and bars represent their frequencies.

C. Because it shows how potassium content is related to a possible lurking variable.

D. Because it displays how the patterns in potassium content could apply in a broader context..

  • What is the shape of the distribution?
  • bimodal
  • bell-shaped
  • right-skewed
  • left-skewed
  • uniform
  • Body Mass Index (BMI) for high-school-aged students are distributed normally with a mean of 21.5 and a standard deviation of 2.1. what percentile does a student fall in if he or she has a BMI of 25?
  • Students in a large statistics class were randomly divided into two groups.The first group tool the midterm exam with a symphony by Mozart Playing in the background, while the second group took the exam with a rock music playing. The scores of the two groups on the exams were compared.What type of study is this?
  • The heights of young women aged 18-24 are approximately normal with a mean of 65 inches and a standard deviation of 2.5 inches. How tall are the tallest 25% of women? (Use the closest percentile that appears in Table B.)
  • -98.21
  • 95.54
  • 93.32
  • 98.21
  • -95.54
  • A matched pairs experiment
  • An observational study based on a stratified sample
  • A randomized block experiment
  • An observation study based on a simple random sample
  • A completely randomized experiment.

A.66.75 inches or more

B.67.50 inches or more

C.68.25 inches or more

D.65.00 inches or more

40. An educator says that the correlation between student’s grades and the type of music they prefer is r=-0.7. This means that

A. Students who prefer classical music tend to have higher grades

B.Student who prefer classical music tend to have lower grades

C.The educator is confused, because correlation makes no sense in this situation.

D.There is almost no association between grades and tastes in music.

  • How does the correlatio coefficient, r, for the data in Plot A compare with the correlation coefficient r, for the data in plot B?
  • The survey of study habitsand attitudes (SSHA) is a psychological test that measures themotivation, and attitudes toward school and study habits of students. Scores range from 0-200. Here are two boxplots of SSHA scores from an SRS of both make and female first year students at a private college.
  • r in Plot A is less than r in Plot B.
  • r in Plot A is greater than r in Plot B
  • Not enough information exists to compare the two r values
  • r in Plot A is equal to r in Plot B .

Which of the following statement is true?

  • The distribution for female scores appears somewhat skewed to the left
  • Fifty percent of the scores for males are between approximately 115 and 142
  • The percentage of male scoring between about 98 and 142 is clearly greater that the percentage of female scoring between about 126 and 154.
  • For males, the mean score should be greater than the median.

43.A local planning commission is interested in finding out what proportion of the city’s residents are opposed to constructing a new baseball stadium in the downtown area. A random sample of 1,870 residents is obtained, and 41.2% of them are opposed to the stadium. A 95% confidence interval was created for the proportion of the city residents that are opposed to constructing a new baseball stadium in the downtown area.By “95 confidence, “ we mean that

  • we are certain that the interval contains the true proportion of all residents that opposed constructing a new stadium in the downtown area.
  • 95% of all educated adults would believe the statement
  • 95% of all residents oppose the construction of a new stadium in the downtown area
  • the method we used to obtain the interval produces intervals containing the true proportion in 95%of all possible sample of the same size.

44.A consumer organization was concerned that an automobile manufacturer was misleading consumer by overstating the average fuel efficiency ( measures in miles per gallon or mpg) of a particular car model. The model was advertisedto get 27 mpg.To investigate, the researcher selected a random sample of 10 cars of that model. Each car was then randomly assigned a different driver. Each car was driven for 5,000 miles, and the total fuel consumption was used to compute the mpg for the car. What is the parameter of interest?

  • The population of all cars of this particular model
  • TheMpg of a single car of this model
  • The population mean mpg of this particular car model
  • The mean mpg of the 10 cars
  • If we took an SRS of 600 Latter-day Saints living in Utah ( out of 2,000,554) and the SRS of the 1000 Latter-day Saints living in the US outside of Utah (out of4, 465, 713) and asked each person whether he or she has given a Book of Mormon to a friend, which sample would have the smaller margin of error for the proportion?

A. US outside Utah, because the sample size (1000) is large than for Utah (600)

  • Utah, because 600/2,000,554 is more than 1,000/4,465,713.
  • Both would be the same, because simple random samples are taken in both places:
  • US outside Utah, because it has a larger population.
  • Utah, because it has a smaller population.
  • To create a good graph, you should try to use three-dimensional effects, mangy colors, and eye-catching backgrounds.

A. True

B. False

  • Seasonal variation in a line graph is a long-term upward or downward movement over time in the pattern of the graph.
  • It is important that government statistics be free from political influence
  • The five-number summary consists of: minimum, Q1, mean, Q3 and the Maximum

A. True

B. False

A. True

B. False

A. True

B. False

  • An index number measures the value of a number relative to its variation.

A. True

B. False

Part 2: SHORT ANSWER AND Easy Questions

Answer completely but concisely.

51.What do we say that “association does not imply causation”? explain and give example.

52. What is extrapolation, and why is it risky? Explain and give an example.

  • These are scores for 10 students on a science exam:

7386 82 80 71 67 46 39 77 89

A) Make a stemplot of the distribution of scores. Briefly describe the shape of t he distribution.

B) Based on the shape of the stemplot, calculate the appropriate measures of center and spread.