Data Analysis Exam II

True

Complementary outcomes are exhaustive of all possible outcomes.

The calculation in the denominator is different.

How is the sample variance computed differently from the population variance?

True

Mathematical expectation can be used to estimate the expected value of variance and standard deviation.

. 0 to +∞

Measures of variability can range in value from

0 to +∞

Measures of variability can range in value from

Approximate

Most behavior is believed to ______ a normal distribution.

The second area is bigger.

State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the right of the mean, or the area between z = ±1.00.

False

A binomial probability distribution is constructed for random variables that have at least two possible outcomes.

True

A binomial probability distribution is the distribution of random outcomes for a bivariate or dichotomous random variable.

binomial probability distribution.

A distribution of probabilities for random outcomes of a bivariate or dichotomous random variable is called a

Variance

A measure of the average squared distance of scores from the mean is called the

1.75

A professor finds that the students scored a 76 ± 8 ( M ± SD) on the final exam. On this exam, a score of 90 is an A. Assuming these data are normally distributed, what is the z score for 90 (the cutoff for an A)?

False

A researcher computes the following scores: 12, 8, 14, 12, and 10. If these scores were substituted into each formula, the sample variance would be smaller than the population variance.

-1.0

A researcher determines that students are active about 60 ± 12 ( M ± SD) min/day. Assuming these data are normally distributed, what is the z score for students being active 48 min/week?

17

A researcher finds that 20 of 120 students failed an exam. In this case, the probability of failing this exam was ______.

Most students drink between 1.5 and 3.1 cups of coffee per study session.

A researcher measures the amount of coffee consumed by college students while studying during the final exam week. In her study, she found that students drink 2.3 ± 0.8 ( M ± SD) cups of coffee per study session. Assuming the data are normally distributed, which of the following is the most appropriate conclusion?

Both samples have the same standard deviation.

A researcher records the following motor assessment scores for two samples of athletes. Which sample has the largest standard deviation? Sample A: 8, 10, 12, 15, and 18 Sample B: 16, 18, 20, 23, and 26

1.0 (9.9 to 8.9)

A researcher records the following scores for an Olympic gymnast following her routine: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8. What is the range for the scores?

33

A researcher records the number of job openings among small businesses. She finds that the probability that a small business has 0 job openings is p = .22; 1 job opening is p = .45; 2 job openings is p = .08; and 3 job openings is p = .25. What is the probability that a small business has at least 2 job openings?

At least 95% of classes were between 68 and 92 decibels.

A researcher records the sound (in decibels) during a series of lessons taught by a substitute teacher at a local elementary school. In his study, he found that the sound was 80 ± 6 ( M ± SD) decibels. Assuming the data are normally distributed, which of the following is an appropriate conclusion?

df = 23; it represents the number of scores that are free to vary in a sample.

A researcher selects a sample of 24 participants and has them complete a survey on dating preferences. In this example, what are the degrees of freedom for sample variance and what does this represent?

All of these

A theoretical distribution that evenly distributes data around the mean, median, and mode is called the

Unbiased estimator

A(n) ________ is a sample statistic that equals a population parameter on average.

the value of sample variance decreases.

All other things being equal (so assuming that the value of SS never changes), as sample size increases,

the top and bottom 25% of scores in a distribution before calculating range.

An interquartile range removes

True

For mutually exclusive outcomes, one or the other outcome can occur (Outcome A or Outcome B), but not both outcomes (Outcome A and Outcome B).

False

If an outcome has a 1 in 100 chance of occurrence, then the probability of that outcome is p = .10.

True

In a normal distribution with 3 ± 1 ( M ± SD), a researcher can appropriately conclude that about 84.13% of scores were greater than 2.

False

In a normal distribution, the mean can only take on positive values.

False

It is appropriate to use the normal approximation of the binomial distribution with a sample of 100 participants, where p = .07 and q = .93.

True

On average, the sample variance will be equal to the population variance only when dividing SS by df.

True

One reason the denominator for sample variance is ( n - 1) is because this makes it an unbiased estimator of the population variance.

True

Suppose a researcher observes a population of 12 people and computes SS = 192. In this example, the standard deviation is 4.

win 0.20 cents per play

Suppose you open a new game at the county fair. When patrons win, you pay them $3.00; when patrons lose, they pay you $1.00. If the probability of a patron winning is p = .20, then how much can you expect to win (or lose) in the long run? Hint: You need to compute the expected value of the mean.

Real limits

The ______ are the range of continuous values containing the score of interest in a binomial distribution.

it produces a minimal positive solution that is not zero, as long as all scores are not exactly the same value.

The advantage of squaring the deviation of each score from the mean and then summing is that

True

The binomial probability distribution is distributed with u=np and o= square root of npq

Equals

The definitional formula ______ the computational formula for SS.

are equal to the sample size minus one.

The degrees of freedom for the sample variance

True

The expected value of a random variable is the mean of a probability distribution.

expected value of the mean and mathematical expectation

The mean of a probability distribution is called the

expected value of the mean and mathematical expectation.

The mean of a probability distribution is called the

True

The mean, median, and mode are all located at the 50th percentile in a standard normal distribution.

scores above the mean are distributed the same as scores below the mean.

The normal distribution is symmetrical, which means that

False

The population standard deviation is equal to 10 when SS = 100 and n = 10.

33

The probability that someone in the human population has blood type AB is about p = .08; the probability that someone has blood type O is about p = .25. Knowing that each individual can have one and only one blood type, what is the probability that a person has an AB or O blood type?

True

The standard deviation is typically reported in research reports with the mean for a data set.

False

The total area under a normal curve increases as the standard deviation increases.

False

The unit normal table can be used to find the probability of a particular score for most, but certainly not all, possible normal distributions.

z score

The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a

True

The z score cutoff for the top 50% of scores in any normal distribution is 0.

±1.96

What is the z score for scores in the top and bottom 2.5%?

False

When a z score equals 0, this means that there is no variability.

0.5

Which of the following is a possible value for the standard deviation of a normal distribution?

Multiplying each score times the same constant will change the standard deviation by that constant.

Which of the following is a property of the standard deviation?

10/80, 23/80, 37/80, 10/80

Which of the following probability distributions is accurate?

The proportion of area between z = +1 and z = -1.

Which of the following proportions is largest in a z distribution?

Doing so makes the sample variance an unbiased estimator of the population variance.

Why is it important to divide by df to compute sample variance?

False

For a set of data with 5 ± 1.5, at least 95% of scores are greater than 3.0.

0.82

Below is the probability distribution for random variable x. What is the probability of at least a score of 2 in this distribution? x 1 2 3 p(x) 0.18 0.42 0.40

All of these

By definition, the probability of an outcome or event is

without squaring each deviation, the solution for SS would be zero.

Each deviation in the numerator for variance is squared because