MOD 5

You have collected a sample with n=30 and calculated that the standard deviation of the sample is 8.06. Calculate the estimate for the standard error of the mean.

1.47

The average length of 1-month-old male infants is 21.52 inches, with a standard deviation of 1.02. At his 1-month check-up, Xander measures 24 inches. What is Xander's z-score? Enter your answer with accuracy to two decimal places.

2.43

The Final Exam in Statistics had a mean completion time of 45 minutes, with a standard deviation of 4 minutes. A student completed his exam in 48 minutes. What percent of students took longer than this student to complete the Final Exam? Enter your answer from the z-Converter with accuracy to one decimal place.

22.7. - HOW?

The average length of 1-month-old male infants is 21.52 inches, with a standard deviation of 1.02. At his 1-month check-up, Kyle measures in the 93.71 percentile. How long is Kyle? Enter your answer with accuracy to two decimal places.

23.08 - HOW?

Based on the General Social Survey (2018), adults usually worked an average of 38.25 hours per week, with a standard deviation of 14.24. If one individual usually worked 41.46 hours, what is his percentile? Enter your answer from the z-Converter with accuracy to one decimal place.

58.9 - HOW?

A discrete probability distribution a. represents the probability of each value of a variable. b. gives the probability of ranges of values under a mathematical function. c. has only two values, p and 1－p. d. describes only contrived events, such as dice rolling. e. both represent the probability of each value of a variable and has only two values, p and 1－p. f. both gives the probability of ranges of values under a mathematical function and describes only contrived even

a

Expected relative frequency refers to a. the observed proportions of large numbers of events. b. hypothetically repeating an experiment a large number of times. c. the complement rule. d. the degree of belief that an event will occur.

a

For a population with a mean of 50 and a standard deviation of 1.5, two sampling distributions are created. Sampling Distribution A uses a sample size of 16 and Sampling Distribution B uses a sample size of 100. Compare the variability of the Original Distribution of scores, Sampling Distribution A, and Sampling Distribution B. a. Original distribution > Distribution A > Distribution B b. Distribution B > Distribution A > Original distribution c. Original distribution = Distribution A = Distrib

a

One characteristic of a normal distribution is a. symmetry. b. skewness. c. asymmetry.

a

Sampling distributions are useful in statistics because they a. can be used to estimate the probability distribution for sampling errors. b. allow us to collect less data than ordinarily required, by a factor of √n. c. allow us to use a computer to simulate the data for our research. d. can be used to standardize the values in a population of observations.

a

This graph shows the distribution of 478 empathy measures from a recent study. Assuming that these data are normally distributed, about how many people would we predict to be within 2 standard deviations of the mean? a. 456 b. 342 c. 479 d. 325

a

Which of the following statements are accurate? a. A z-score of -1 and z-score of 1 are the same distance from the mean. b. It is not possible to have a z-score of -5. c. In the standard normal distribution, most of the scores are between z = 1 and z = 2. d. A z-score of 1.5 always represents a higher raw score than a z-score of -1.5.

a

2. Probability is an important consideration in statistics a. because observations are typically not independent. b. because of randomness introduced by sampling. c. as a way of generating sample data sets. d. as a way of summarizing a set of data.

b

In a normal distribution, most of the observations are found a. toward the edges of the distribution. b. in or near the center of the distribution. c. nearer the left (lower) end of the distribution. d. nearer the right (higher) end of the distribution.

b

In the standard normal distribution, which z-score would be least likely to occur by chance (i.e. have the smallest probability)? a. A z-score between -1 and 1. b. A z-score greater than 3. c. A z-score smaller than -2 d. A z-score between 0 and 2.

b

The central limit theorem makes what possible for applications of statistics? a. It determines the number of participants to sample for a study. b. It allows researchers to test ideas from variables with any type of distribution. c. It tells researchers the optimum number of samples to create a normal distribution. d. It provides the formula for the area under a normal distribution.

b

What is the percentage of scores between -2σ and +2σ? a. 64.2% b. 95.4% c. 47.7% d. 99.8%

b

Which is true of the standard error of the mean? a. It increases as n increases. b. It is a parameter of a distribution made up of statistics. c. It is a statistic for a distribution made up of observations. d. It decreases as 𝜎X increases.

b

As long as n > 1, which of the following best describes the relation between the standard deviation of the distribution of scores and the standard deviation of the sampling distribution of means? a. The variance for the distribution of scores will be smaller. b. The variances of the two distributions will be equal. c. The variance for the sampling distribution of means will be smaller. d. Impossible to know. For some samples, one will be larger. For other samples, the other will be larger.

c

As the ______ increases, the sampling distribution of the means becomes more and more normally distributed. a. population mean b. population standard deviation c. sample size d. sample variability

c

In a normal distribution, approximately what percentage of observations will be beyond 2 standard deviations of the mean? a. 16% b. 34% c. 5% d. 95%

c

Mariah received a z-score of 1.8 on her Biology test. Interpret this z-score. a. Mariah scored 1.8 standard deviations below the population mean. b. Mariah's score is within ±1.8 points of the population mean score. c. Mariah scored 1.8 standard deviations above the population mean. d. Mariah's score is 1.8 points higher than the average exam score.

c

The distribution of exam scores in a population is normal with a mean of 81 points and a standard deviation of 2.2. Under what conditions would a sampling distribution of means approximate the shape of a normal distribution? a. When n = 30 or more b. When n = 100 or more c. The sampling distribution will always approximate the shape of the normal distribution. d. The sampling distribution will never approximate the shape of the normal distribution.

c

The probability of an event equals _____ divided by the number of possible outcomes. a. the number of dependent outcomes b. the number of possible events c. the number of outcomes in an event set d. the number of independent outcomes

c

You have conducted a study with n = 10 and now plan a follow-up study. In the follow-up, you have decided that you would like to cut the standard error of the mean in half. What should your n be for the second study? a. 5 b. 20 c. 40 d. 100

c

In order to identify which student performed the best on a statistics exam among four different sections of the course, an instructor converted all student scores to z-scores. Based on the standard normal distribution, which student performed the best? a. The student with a z-score of 0.5. b. The student with a z-score of -1.95. c. The student with a z-score of -0.1. d. The student with a z-score of 1.5.

d

Which of the following are part of the central limit theorem? a. The mean of the sampling distribution of means is smaller than the mean of the population of scores. b. For sampling distributions to resemble the normal distribution, sample size should always be at n = 30 or higher. c. The variability of the sampling distribution of means will always be larger than that of the population of scores. d. For a skewed population, as sample size increases, the sampling distribution will more closely a

d

Sampling error is a. the difference between a sample statistic and the population parameter. b. introduced by sampling without replacement. c. usually unknown. d. entirely avoidable if samples are correctly designed. e. both the difference between a sample statistic and the population parameter and usually unknown. f. both introduced by sampling without replacement and entirely avoidable if samples are correctly designed.

e

Sampling distribution

Frequency distribution of sample statistics

Standard normal distribution

Normal distribution with mean 0 and standard deviation 1

z-Score distribution

Normal distribution with mean 0 and standard deviation 1

z-Score

Number of standard deviations a score is from the mean

Percentile

Percentage of population below a particular z-score

Outcome

Possible result of a random process

Complement Rule

Probability of other events is 1 minus probability of Event A

Expected relative frequency

Proportion of occurrence of an event in a large number of repetitions

Probability Distribution

Representation of a set of probabilities

Simple random sample

Sample where every subset is equally likely

Sampling with replacement

Sample where observations are returned to population after selection

Event

Set of outcomes from a process

Process

Set of rules determining a result

Standard error of the mean (SEM)

Standard deviation of sampling distribution of means

Probability

Value between 0 and 1 representing long-run relative frequency

The scores on a physics exam are normally distributed with a mean of 83 and a standard deviation of 1.5. What is the minimum score a student would need to earn to be in the top 13 percent of scores? Enter your answer with accuracy to two decimal places.

84.70

Patrick recently took the ACT and earned a z-score of 2.88. What is his percentile? Enter your answer from the z-Converter with accuracy to one decimal place.

99.8

Normal distribution

Bell-shaped curve

Sampling Error

Difference between sample statistic and population parameter

Central limit theorem

Distribution of means approximates normal distribution

Independent

Events have no influence on each other