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fundamentals of statistics
Questions and Answers of
Fundamentals Of Statistics
Why does the normal curve table only cover half of the standard normal distribution?
How do you determine the area of the standard normal distribution that is between the mean and a stated z-score? Less or greater than a z-score? Between two z-scores?
What percentage of the standard normal distribution lies within one, two, and three standard deviations of the mean?
Using the normal curve table, determine the area of the standard normal distribution that is between the mean of .00 and the following z-scores:a. z = .46b. z = 1.30c. z = 2.87d. z = −.19e. z =
Using the normal curve table and the rules in Table 5.2, determine the area of the standard normal distribution that is either less () than the following z-scores:a. z < .66b. z < 2.55c. z < −.75d.
Using the normal curve table and the rules in Table 5.2, determine the area of the standard normal distribution that is between the following z-scores.a. z = .25 and z = .50b. z = 1.33 and z = 2.25c.
Why might one want to apply the standard normal distribution to a normal distribution?
What’s the first step in applying the standard normal distribution to a normal distribution?
Transform the following lengths of pregnancy into z-scores:a. 275 daysb. 280 daysc. 265 daysd. 286 dayse. 260 days A study of more than 1,000 pregnant women in India found the length of pregnancy was
What percentage (%) of pregnancies . . .a. is shorter than 277 days?b. is shorter than 262 days?c. is longer than 270 days?d. is longer than 283 days?e. is between 279 and 286 days?f. is between 268
What percentage (%) of iPods . . .a. has a likelihood of failure greater than 25%?b. has a likelihood of failure greater than 10%?c. has a likelihood of failure less than 20%?d. has a likelihood of
What are the differences between calculating z-scores for normal distributions versus frequency distributions?
What are common reasons for standardizing frequency distributions?
What are the main characteristics of standardized distributions?
Does standardizing a frequency distribution create a normal distribution? Why or why not?
Under what conditions could you apply the normal curve table to a standardized distribution?
Using the descriptive statistics calculated in Table 5.4, calculate standardized scores for the number of remarks variable for the following members.a. Member 4 (# remarks = 25)b. Member 5 (# remarks
Imagine you take a quiz in one of your classes and learn that the class mean(X)was 15.53 and the standard deviation (s) was 4.22. Calculate standardized scores for the following quiz scores.a. 14b.
You play on a softball team and at the end of the season find the batting averages of the players on your team are as follows:a. Calculate the mean(X) and standard deviation (s) of the batting
Transform the following IQ scores into z-scores.a. 116b. 84c. 124d. 95e. 130 IQ scores are normally distributed in the population with a mean (μ) of 100 and a standard deviation (σ) of 16. Use the
What percentage of IQ scores is between the mean of 100 and . . .a. 116b. 68c. 105d. 90e. 140 IQ scores are normally distributed in the population with a mean (μ) of 100 and a standard deviation
What percentage of IQ scores is . . .a. less than 122b. less than 77c. less than 104d. greater than 135e. greater than 73f. greater than 112 IQ scores are normally distributed in the population with
What percentage of IQ scores is . . .a. between 115 and 130b. between 105 and 120c. between 75 and 85d. between 80 and 95e. between 90 and 110f. between 80 and 120 IQ scores are normally distributed
What percentage of IQ scores is . . .a. less than 110 or greater than 130b. less than 80 or greater than 90c. less than 95 or greater than 105d. less than 84 or greater than 116 IQ scores are
A researcher constructs a test to measure self-esteem. In doing so, she calculates a mean for her sample of 10 with a standard deviation of 2. Assuming that scores on this test in the larger
What percentage of the video games is built . . .a. in less than 15 minutesb. in less than 10 minutesc. in more than 20 minutesd. in more than 30 minutese. between 26 and 32 minutesf. between 12 and
Five percent of the video games (the bottom 5%) take less than ____ minutes to build.Imagine you are the president of a toy company that builds video games. You have determined that the time needed
Ninety percent of the video games (the top 90%) are built in ____ minutes.Imagine you are the president of a toy company that builds video games. You have determined that the time needed to build
How many base hits can a baseball team expect to get in a game? Frohlich (1994) recorded the number of hits by the 28 Major League Baseball teams for all of the games played from 1989 to 1993 (each
In another baseball-related story, between 1980 and 2000, there was a remarkable increase in the number of home runs hit in the major leagues. A recent article stated that the average number of home
What if you took midterms in two different courses and happened to get the same grade of 68 on both of them. In the first course, the mean was 63 and the standard deviation was 10. In the second
What if you took final examinations in two different courses and happened to get the same grade of 72 on both of them? The mean in the two courses turns out to be the same (= 60). However, the
The mean of the Graduate Record Examination (GRE), for the verbal section, is 500 with a standard deviation of 100. Your friend scores a 529.a. What percentage of test takers did she score above?b.
Two students are comparing their recent midterm scores. The first student received a 92 and the second student received an 86. However, they are in different classes, and their tests were slightly
You collect the grade point average (GPA) from 10 students:a. Calculate the mean (X ) and standard deviation (s) of these GPAs.b. Calculate the z-score for each GPA in order to standardize the
What is probability (conceptually and mathematically)?
Why is probability important to researchers?
What is the addition rule of probability?
What is the relationship between sampling error and probability?
How can probability be applied to distributions?
What is the difference between normal distributions and binomial distributions?
Here is a set of scores: 7 2 6 1 9 3 5 2. If we were to randomly select one of these scores, what is the probability this score will be . . .a. equal to 6b. equal to 2c. greater than 4d. less than
Using the standard normal distribution and the normal curve table, what is the probability of a z-score . . .a. greater than 1.25b. less than .40c. greater than −.50d. less than −1.33e. between
According to the National Center for Health Statistics, in 2005 the average birth weight of a newborn baby was approximately normally distributed with a mean of 119 ounces (7 pounds, 7 ounces) and a
What are the main steps in hypothesis testing?
What are the differences between research hypotheses and statistical hypotheses?
What are the null and the alternative hypotheses?
What are the main steps in making the decision about the null hypothesis?
What is the difference between the region of rejection and the region of nonrejection?
Does the value of a statistic that exceeds the critical value have a low or high probability of occurring?
In stating the conclusion of a statistical analysis, what information is useful to provide?
Imagine you decide to conduct a study to test each of the following statements. For each one, state a null and alternative hypothesis (H0 and H1).a. A survey of iPod owners conducted in 2005
Returning to the Super Bowl example, imagine you draw a sample of 20 teams (N = 20) rather than 12. For this situation,a. State the null and alternative hypotheses (H0 and H1).b. Identify the
A friend of yours claims to have extrasensory perception (ESP). You test this by creating a deck of 16 cards, half of which are red and the other half green. Sitting behind a partition, you hold up
Within hypothesis testing, why do we say a research hypothesis has been "supported" rather than "proved"?
What are the two types of errors you can make regarding the two statistical hypotheses?
What are the three factors discussed in this chapter that affect the decision about the null hypothesis? In what specific ways does each of these influence this decision?
What is the difference between a directional (one-tailed) and a nondirectional (two-tailed) alternative hypothesis? Under what research situations might you use one versus the other?
Using the Super Bowl example, imagine you draw the following three samples. Use the binomial probabilities table to determine the critical values (assume the alternative hypothesis is nondirectional
Returning to the Super Bowl example, imagine you draw the following three samples. Use the binomial probabilities table to determine the critical values for a .05 and a .01 (assume the alternative
Returning to the Super Bowl example, imagine you draw the following three samples. Use the binomial probabilities table to determine the critical values for a nondirectional alternative hypothesis
A friend of yours asks 20 people to rate a movie using a 1- to 5-star rating: the higher the number of stars, the higher the recommendation. Their ratings are listed below:a. What is the probability
For the standard normal distribution, what is the probability of having a z-score . . .a. greater than 1.67 (z > 1.67)b. greater than −1.67 (z > −1.67)c. less than .75 (z < .75)d. less than
According to the test’s publishers (www.act.org), scores on the ACT college entrance examination for students graduating in 2001 were normally distributed, with μ = 21 and σ = 5 (scores can range
A bottling company uses a machine to fill 16-ounce bottles with orange juice. The company finds that the standard deviation of the amount of juice in these bottles is equal to 1/4 ounce (σ = .25).
The length of time, in days, of pregnancy in healthy women is approximately normally distributed, with μ = 280 days and σ = 10 days. What is the probability a woman will . . .a. give birth more
(This example was introduced in Chapter 5.) How many base hits can a baseball team expect to get in a game?Frohlich (1994) recorded the number of hits by the 28 Major League Baseball teams for all of
Assuming a coin is fair, in a sample of 6 coin flips, what is the probability of getting . . .a. 3 headsb. less than 4 headsc. more than 2 heads and less than 5 heads TABLE 6.5 CALCULATION OF
For a family with 5 children, assuming the probability of having a boy and having a girl are both .50 (50%), what is the probability of having . . .a. 0 boysb. 2 boysc. more than 3 boys TABLE 6.5
Assume an equal number of people prefer the two most popular brands of cola. Under this assumption, what is the probability of the following claim being true: “9 out of 10 people prefer Brand X
In each of four political races, Democrats are believed to have a 60% chance of winning. If so, what is the probability that Democrats will win . . .a. none of the electionsb. at least one electionc.
A store advertises that there is a 90% chance their equipment will be trouble-free for a year. If you buy 6 of their products, what is the probability that . . .a. all of the products will be
Assuming that 35% of all marriages end in divorce, if you encountered 8 adult men, what is the probability that all of them are still married? TABLE 6.5 CALCULATION OF CRITICAL VALUES FOR BINOMIAL
For each of the following situations, state the two competing hypotheses to be tested using words rather than mathematical symbols or formulas.a. A company designs a program aimed at helping people
For each of the following situations, state the two competing hypotheses to be tested using words rather than mathematical symbols or formulas.a. Students who are taught effective learning skills
For each of the following situations, state a null hypothesis (H0) and a nondirectional (two-tailed) alternative hypothesis (H1).a. A bank advertises that customers never have to wait more than 5
Returning to the Super Bowl example discussed earlier in this chapter, imagine that you found 13 of 18 teams that won the coin flip went on to win the game.a. State the null and alternative
Two researchers test the same research hypothesis using the same instruments. One researcher rejects the null hypothesis but the other does not.a. Which researcher is more likely to have had a larger
A company makes a test they say can detect whether or not someone is guilty of a crime. In this situation, what are the two types of errors that could be made?
How could you create the sampling distribution of the mean for a variable?
What are the main characteristics (modality, symmetry, variability) of the sampling distribution of the mean?
What is measured by the standard error of the mean?
Why is it important that the sampling distribution of the mean is normally distributed?
In testing one mean, the value of what parameter is stated in the null and alternative hypotheses?
In testing one mean, what is implied by the null and alternative hypotheses?
Why are nondirectional (two-tailed) rather than directional (one-tailed) alternative hypotheses predominantly used in research studies?
What are the similarities and differences between the formula for the z-score (Chapter 5) and the z-test for one mean?
Under what conditions would one calculate the population standard error of the mean rather than the standard error of the mean?
What two factors influence the amount of variability in a distribution of sample means?
For each of the following situations, calculate the population standard error of the mean (σX̅) .a. σ = 12.00; N = 16b. σ = 1.00; N = 9c. σ = 4.50; N = 26d. σ = 39.76; N = 50
For each of the following situations, calculate the z-statistic (z).a. X̅ = 10.00; μ = 8; = 3; N = 9b. X̅ = 4.00; μ = 7; = 6; N = 16c. X̅ = 3.52; μ = 3.29; = 1.18; N = 21d. X̅ = 13.25;
What is the difference between a statistic that is statistically “significant” and one that is “nonsignificant”?
What is the difference between a statistic referred to as “nonsignificant” and one referred to as“insignificant”?
Does “p < .05” imply the null hypothesis was rejected or not rejected? Why?
When and why would you determine whether the probability of a statistic is less than .01?
Which of these would you use when the value of a statistic falls in between the .05 and .01 critical values:p > .05, p < .05, or p < .01?
What information about a statistical analysis is typically included when communicating the results of the analysis?
What are some assumptions applicable to the z-test for one mean?
For each of the following situations, calculate the z-statistic (z), make a decision about the null hypothesis(reject, do not reject), and indicate the level of significance (p > .05, p < .05, p <
For each of the following situations, calculate the population standard error of the mean (σX̅) and the z-statistic (z), make a decision about the null hypothesis, and indicate the level of
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