Week 1 to Week 4 statistics

(HW4) What is the probability of the following.(b) An event B that is impossible?

0

(HW4) From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

0.005

(HW4) A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

0.02

(HW4) A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:

0.04

(HW4) What is the probability of getting a sum 9 from two throws of a dice?

0.11

(HW4) Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

0.13

(HW4) A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head.

0.25

(HW4) In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

0.2757 and 0.2957

(HW4) In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

0.33

(HW4) A fair six sided die is rolled. What is the probability of getting 5 or 6 on a single throw? (Enter your answer to 3 decimal places.)

0.333

(HW4) Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

0.45

(HW4) In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

0.46

(HW4) A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

0.48

(HW4) A fair six sided die is rolled. What is the probability of getting a number less than 5 on a single throw? (Enter your answer to 3 decimal places.)

0.667

(HW4) Suppose the newspaper states that the probability of rain today is 15%.What is the probability of the complement? (Convert % to proportion and enter your answer to two decimal places.)

0.85

(HW4) Three unbiased coins are tossed. What is the probability of getting at most two heads?

0.88

(HW4) A die is rolled, find the probability that the number obtained is less than 9.

1

(HW4) What is the probability of the following.(a) An event A that is certain to occur?

1

(HW2) In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. (a) Consider the following data set.8, 13, 14, 9, 9, and compute s. (b) Add 4 to each data value to get the new data set 12, 17, 18, 13, 13. Compute s. Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

Adding the same constant c to each data value results in the standard deviation remaining the same.

(HW4) What is the law of large numbers?

As the sample size increases, the relative frequency of outcomes gets closer to the theoretical probability of the outcome.

(HW4) Suppose the newspaper states that the probability of rain today is 15%.What is the complement of the event "rain today"? A) rain yesterday B) rain tomorrow C) no rain today D) no rain tomorrow

C) no rain today

(HW 1) Methods for summarizing data make up the branch of statistics called inferential statistics.

False

(HW 1) The entire collection of individuals or objects about which information is desired is called a sample.

False

(HW 1)A bar chart is a useful graphical tool for describing the shape of the distribution of a categorical variable.

False

(HW 1)A data set is multivariate if it consists only of numeric variables.

False

(HW 1)A pie chart is most useful for numeric data.

False

(HW 1)The relative frequency for a particular category is the number of times the category appears in the data.

False

(HW2) For data that is skewed to the right, Sum(x-xbar)>0

False

(HW2) The density of a class can be calculated by multiplying the relative frequency of the class times the class width.

False

(HW2) The median is the middle value of an unordered data set.

False

(HW2) The variance is the positive square root of the standard deviation.

False

(HW3) The higher the value of the correlation coefficient, the greater the evidence for a causal relationship between x and y.

False

(HW3) The value of Pearson's r is always between 0 and 1.

False

(HW4) Any collection of possible outcomes of a chance experiment is called a sample space.

False

(HW4) If two events, A and B, are disjoint, then P(A&B)=P(A)*P(B)

False

(HW4) The event "A or B" consists of all of the outcomes common in both of the events.

False

(HW3) When using the leasts-quares line for prediction, are results more reliable for extrapolation or interpolation?

Interpolation, because we are predicting from data in the range used to create the least-squares line.

(HW4) If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.

It would be better to use 500 trials, because the law of large numbers would take effect.

(HW2) How does the mean (or median or mode) change if each data value is multiplied by a constant c?

Multiplying each data value by the same constant c results in the mean being multiplied by c.

(HW2) In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. (a) Consider the following data set.7, 16, 11, 11, 11, and compute s. (b) Multiply each data value by 6 to obtain the new data set 42, 96, 66, 66, 66. Compute s. (c) Multiply each data value by -6 to obtain the new data set -42, -96, -66, -66, -66. Compute s. Compare the results of parts (a), (b) and (c). In general, how does the standard deviation change if each data valueis multiplied by a constant c?

Multiplying each data value by the same constant c results in the standard deviation being |c|times as large.

(HW2) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.9 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? (Refer to the previous problem) Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to 2 decimal places.)

No, 4.64

(HW2) One indicator of an outlier is that an observation is more than 3 standard deviations from the mean. Consider the data value 80. If a data set has mean 70 and standard deviation 4, is 80 a suspect outlier?

No, since 80 is less than 3 standard deviations above the mean.

(HW3) Over the past few years, there has been a strong positive correlation between the annual consumption of diet soda drinks and the number of traffic accidents.Do you think increasing consumption of diet soda drinks causes traffic accidents?

No. A strong correlation does not imply causation.

(HW2) If the highest number were increased, what would be the effect on the median and mean (sample size n>2)?

The mean would increase while the median would remain the same.

(HW2) When a distribution is mound-shaped symmetrical, what is the general relationship among the values of the mean, median and mode?

The mean, median, and mode are approximately equal.

(HW3) Suppose two variables are negatively correlated. Does the response variable increase or decrease on an average as the explanatory variable increases?

The response variable will decrease as the explanatory variable increases.

(HW3) Suppose two variables are positively correlated. Does the response variable increase or decrease on an average as the explanatory variable increases?

The response variable will increase as the explanatory variable increases.

(HW3) Examine the computation formula for r, the sample correlation coefficient. If we have a set of x and y data values and we exchange corresponding x and y values to get a new data set, should the sample correlation coefficient be the same for both sets of data? Explain your answer.

The result is the same because the formula is not dependent on which values are the x values and which values are the y values.

(HW2) How do you think the mode, median, and mean are affected when the same constant is added to each data value in a set?

There is no distinct pattern when the same constant is added to each data value in a set.

(HW 1)A data set is discrete if the possible values are isolated points on the number line.

True

(HW 1)A primary use of inferential statistics is to make generalizations from a sample to a population.

True

(HW 1)Bar charts should be used with categorical data.

True

(HW2) According to Chebyshev's rule, the fraction of observations that are within 3 standard deviations of the mean is at least eight-ninths.

True

(HW2) An outlier is an unusually small or large data value.

True

(HW2) By definition, an outlier is "extreme" if it is more than 3.0 IQR away from the closest quartile.

True

(HW2) For any given data set, the median must be greater than or equal to the lower quartile, and less than or equal to the upper quartile.

True

(HW2) If the upper (right) tail of a distribution stretches out farther than the lower (left) tail, the distribution is right skewed.

True

(HW2) One advantage of histograms is that they may be used for large data sets.

True

(HW2) One disadvantage of using the mean as a measure of center for a data set is that its value is affected by the presence of even a single outlier in the data set.

True

(HW2) The interquartile range is resistant to the effect of outliers.

True

(HW2) The square root of the sample size often gives a rough estimate of the appropriate number of intervals in a histogram.

True

(HW3) If on average y increases as x increases, the correlation coefficient is positive.

True

(HW3) If r is close to 1, then the points lie close to a straight line with a positive slope.

True

(HW3) The slope of the least squares line is the average amount by which y increases as x increases by one unit.

True

(HW4) A chance experiment is any activity or situation in which there is uncertainty concerning which of two or more possible outcomes will result.

True

(HW4) An event consisting of exactly one outcome is called a simple event.

True

(HW4) Two events are said to be disjoint or mutually exclusive when they have no outcomes in common.

True

(HW3) When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

We are extrapolating. We must consider that the pattern may change outside the data set.

(HW3) In the least-squares line Y^ = 5 - 10x.When x changes by 1 unit, by how much does y change?

When x increases by 1 unit, y decreases by 10 units.

(HW2) If a data set has mean 95 and standard deviation 4, is 80 a suspect outlier?

Yes, since 80 is more than 3 standard deviations below the mean.

(HW2) When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population? Explain. (Here n: sample size, N: population size)

Yes. The formula for s is divided by n, while the formula for σ is divided by N-1.

(HW3) When drawing a scatter diagram, along which axis is the explanatory variable placed? Along which axis is the response variable placed?

horizontal axis; vertical axis

(HW3) Describe the relationship between two variables when the correlation coefficient r is one of the following.(a) near -1

strong negative linear correlation

(HW3) Describe the relationship between two variables when the correlation coefficient r is one of the following.(c) near 1

strong positive linear correlation

(HW2) What does a Z-score measure?

the number of standard deviations a measurement is from the mean

(HW3) Describe the relationship between two variables when the correlation coefficient r is one of the following.(b) near 0

weak or no linear correlation