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mathematics
statistics
Questions and Answers of
Statistics
A population consists of the following N = 5 scores: 0, 6, 4, 3, and 12.a. Compute m and σ for the population.b. Find the z-score for each score in the population.c. Transform the original
A sample consists of the following n = 6 scores: 2, 7, 4, 6, 4, and 7. a. Compute the mean and standard deviation for the sample. b. Find the z-score for each score in the sample. c. Transform the
A distribution has a standard deviation of σ = 6. Describe the location of each of the following z-scores in terms of position relative to the mean. For example, z = +1.00 is a location that is 6
For a population with µ = 50 and σ = 8,a. Find the z-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need
For a population with µ = 40 and σ = 7, find the z-score for each of the following X values. (You probably will need to use a formula and a calculator to find these values.)
For a population with a mean of ( = 100 and a standard deviation of ( = 12,a. Find the z-score for each of the following X values.b. Find the score (X value) that corresponds to each of the following
A population has a mean of µ = 40 and a standard deviation of σ = 8.a. For this population, find the z-score for each of the following X values.b. For the same population, find the score (X value)
A sample has a mean of M = 40 and a standard deviation of s = 6. Find the z-score for each of the following X values from this sample.
A sample has a mean of M = 80 and a standard deviation of s = 10. For this sample, find the X value corresponding to each of the following z-scores.
A local hardware store has a "Savings Wheel" at the checkout. Customers get to spin the wheel and, when the wheel stops, a pointer indicates how much they will save. The wheel can stop in any one of
Find the z-score location of a vertical line that separates a normal distribution as described in each of the following. a. 20% in the tail on the left b. 40% in the tail on the right c. 75% in the
Find the z-score boundaries that separate a normal distribution as described in each of the following. a. The middle 20% from the 80% in the tails. b. The middle 50% from the 50% in the tails. c. The
For a normal distribution with a mean of μ = 80 and a standard deviation of σ = 20, find the proportion of the population corresponding to each of the following scores.a. Scores greater than 85.b.
A normal distribution has a mean of μ = 50 and a standard deviation of σ = 12. For each of the following scores, indicate whether the tail is to the right or left of the score and find the
IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ = 15. Find the proportion of the population in each of the following IQ
The distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. For the population of students who have taken the SAT,a. What proportion
The distribution of SAT scores is normal with μ = 500 and σ = 100.a. What SAT score, X value, separates the top 15% of the distribution from the rest?b. What SAT score, X value, separates the top
A recent newspaper article reported the results of a survey of well-educated suburban parents. The responses to one question indicated that by age 2, children were watching an average of μ = 60
Information from the Department of Motor Vehicles indicates that the average age of licensed drivers is μ = 45.7 years with a standard deviation of σ = 12.5 years. Assuming that the distribution of
A consumer survey indicates that the average household spends μ = $185 on groceries each week. The distribution of spending amounts is approximately normal with a standard deviation of σ = $25.
A psychology class consists of 14 males and 36 females. If the professor selects names from the class list using random sampling, a. What is the probability that the first student selected will be a
Over the past 10 years, the local school district has measured physical fitness for all high school freshmen. During that time, the average score on a treadmill endurance task has been μ = 19.8
Rochester, New York, averages μ = 21.9 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard deviation of σ = 6.5 inches. This year,
A multiple-choice test has 48 questions, each with four response choices. If a student is simply guessing at the answers, a. What is the probability of guessing correctly for any question? b. On
A true/false test has 40 questions. If a students is simply guessing at the answers, a. What is the probability of guessing correctly for any one question? b. On average, how many questions would the
A roulette wheel has alternating red and black numbered slots into one of which the ball finally stops to determine the winner. If a gambler always bets on black to win, what is the probability of
One test for ESP involves using Zener cards. Each card shows one of five different symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card
A trick coin has been weighted so that heads occurs with a probability of p = 2/3, and p(tails) = 1/3. If you toss this coin 72 times, a. How many heads would you expect to get on average? b. What is
For a balanced coin: a. What is the probability of getting more than 30 heads in 50 tosses? b. What is the probability of getting more than 60 heads in 100 tosses? c. Parts a and b both asked for the
A national health organization predicts that 20% of American adults will get the flu this season. If a sample of 100 adults is selected from the population, a. What is the probability that at least
What are the two requirements that must be satisfied for a random sample? Discuss.
What is sampling with replacement, and why is it used?
Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the tail is on the right or left side of the line and find the proportion in the
Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the
Find each of the following probabilities for a normal distribution. a. p(z > 0.25) b. p(z > - 0.75) c. p(z < 1.20) d. p(z < - 1.20)
What proportion of a normal distribution is located between each of the following z-score boundaries? a. z = - 0.50 and z = + 0.50 b. z = - 0.90 and z = + 0.90 c. z = - 1.50 and z = + 1.50
Find each of the following probabilities for a normal distribution. a. p(-0.25 < z < 0.25) b. p(-2.00 < z < 2.00) c. p(-0.30 < z < 1.00) d. p(-1.25 < z < 0.25)
Briefly define each of the following: a. Distribution of sample means b. Expected value of M c. Standard error of M
For a population with a mean of μ = 80 and a standard deviation of σ = 12, find the z-score corresponding to each of the following samples.a. M = 83 for a sample of n = 4 scoresb. M = 83 for a
A sample of n = 4 scores has a mean of M = 75. Find the z-score for this sample:a. If it was obtained from a population with μ = 80 and σ = 10.b. If it was obtained from a population with μ = 80
A population forms a normal distribution with a mean of μ = 80 and a standard deviation of σ = 15. For each of the following samples, compute the z-score for the sample mean and determine whether
A random sample is obtained from a normal population with a mean of μ = 30 and a standard deviation of σ = 8. The sample mean is M = 33.a. Is this a fairly typical sample mean or an extreme value
The population of IQ scores forms a normal distribution with a mean of μ = 100 and a standard deviation ofσ = 15. What is the probability of obtaining a sample mean greater than M = 97,a. for a
The scores on a standardized mathematics test for 8th-grade children in New York State form a normal distribution with a mean of μ = 70 and a standard deviation of σ = 10.a. What proportion of the
A population of scores forms a normal distribution with a mean of μ = 40 and a standard deviation of σ = 12.a. What is the probability of randomly selecting a score less than X = 34?b. What is the
A population of scores forms a normal distribution with a mean of μ = 80 and a standard deviation of σ = 10.a. What proportion of the scores have values between 75 and 85?b. For samples of n = 4,
At the end of the spring semester, the Dean of Students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the
The machinery at a food-packing plant is able to put exactly 12 ounces of juice in every bottle. However, some items such as apples come in variable sizes so it is almost impossible to get exactly 3
Describe the distribution of sample means (shape, expected value, and standard error) for samples of n = 36 selected from a population with a mean of μ = 100 and a standard deviation of σ = 12?
The average age for licensed drivers in the county is μ = 40.3 years with a standard deviation of σ = 13.2 years.a. A researcher obtained a random sample of n = 16 parking tickets and computed an
People are selected to serve on juries by randomly picking names from the list of registered voters.The average age for registered voters in the county is μ = 44.3 years with a standard deviation of
Welsh, Davis, Burke, and Williams (2002) conducted a study to evaluate the effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance. Experienced athletes were given
In the Preview section for this chapter, we discussed a research study demonstrating that 8-month-old infants appear to recognize which samples are likely to be obtained from a population and which
A sample is selected from a population with a mean of μ = 40 and a standard deviation of σ = 8.a. If the sample has n = 4 scores, what is the expected value of M and the standard error of M?b. If
The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?
A population has a standard deviation of σ = 30.a. On average, how much difference should exist between the population mean and the sample mean for n = 4 scores randomly selected from the
For a population with a mean of μ = 70 and a standard deviation of σ = 20, how much error, on average, would you expect between the sample mean (M) and the population mean for each of the following
For a population with a standard deviation of σ = 20, how large a sample is necessary to have a standard error that is:a. Less than or equal to 5 points?b. Less than or equal to 2 points?c. Less
If the population standard deviation is σ = 8, how large a sample is necessary to have a standard error that is:a. Less than 4 points?b. Less than 2 points?c. Less than 1 point?
For a sample of n = 25 scores, what is the value of the population standard deviation (() necessary to produce each of the following a standard error values? a. (M = 10 points? b. (M = 5 points? c.
In the z-score formula as it is used in a hypothesis test,a. Explain what is measured by M - µ in the numerator.b. Explain what is measured by the standard error in the denominator?
Miller (2008) examined the energy drink consumption of college undergraduates and found that males use energy drinks significantly more often than females. To further investigate this phenomenon,
A random sample is selected from a normal population with a mean of µ = 40 and a standard deviation of σ = 10. After a treatment is administered to the individuals in the sample, the sample mean is
There is some evidence that REM sleep, associated with dreaming, may also play a role in learning and memory processing. For example, Smith and Lapp (1991) found increased REM activity for college
There is some evidence indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman, 2008). In a similar study, a
A psychologist is investigating the hypothesis that children who grow up as the only child in the household develop different personality characteristics than those who grow up in larger families. A
A researcher is testing the hypothesis that consuming a sports drink during exercise improves endurance. A sample of n = 50 male college students is obtained and each student is given a series of
Montarello and Martins (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore
Researchers have often noted increases in violent crimes when it is very hot. In fact, Reifman, Larrick, and Fein (1991) noted that this relationship even extends to baseball. That is, there is a
A researcher plans to conduct an experiment testing the effect of caffeine on reaction time during a driving simulation task. A sample of n = 9 participants is selected and each person receives a
A sample of n = 40 is selected from a normal population with µ = 75 msec. and σ = 12, and a treatment is administered to the sample. The treatment is expected to increase scores by an average of 4
The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the
Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant. a. The size of the z-score in a hypothesis test. b. The size of Cohen's
Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant. a. Increasing the alpha level from .01 to .05. b. Changing from a
A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140. For this population, systolic scores average
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of µ = 80 and a standard deviation of σ = 20. The researcher
In words, define the alpha level and the critical region for a hypothesis test?
If the alpha level is changed from α = .05 to α = .01, a. What happens to the boundaries for the critical region? b. What happens to the probability of a Type I error?
Although there is a popular belief that herbal remedies such as ginkgo biloba and ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled
Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden- Chapman, Martin, & Kawachi, 2006). In
A local college requires an English composition course for all freshmen. This year they are evaluating a new online version of the course. A random sample of n = 16 freshmen is selected and the
A random sample is selected from a normal population with a mean of µ = 50 and a standard deviation of σ = 12. After a treatment is administered to the individuals in the sample, the sample mean is
A random sample of n = 36 scores is selected from a normal population with a mean of µ = 60. After a treatment is administered to the individuals in the sample, the sample mean is found to be M =
Find each of the requested values for a population with a mean of µ = 40 and a standard deviation of σ = 8.a. What is the z-score corresponding to X = 52?b. What is the X value corresponding to z =
A survey of female high school seniors shows that the average amount of time spent on clothes, hair, and makeup each morning before school is µ = 35 minutes. Assume that the distribution of
Brunt, Rhee, and Zhong (2008) surveyed 557 undergraduate college students to examine their weight status, health behaviors, and diet. Using body mass index (BMI), they classified the students into
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Discuss.
A random sample of n = 16 individuals is selected from a population with μ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M =
The spotlight effect refers to overestimating the extent to which others notice your appearance or behavior, especially when you commit a social faux pas. Effectively, you feel as if you are suddenly
Many animals, including humans, tend to avoid direct eye contact and even patterns that look like eyes. Some insects, including moths, have evolved eye-spot patterns on their wings to help ward off
Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety
The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a sample of n = 30 books and records the
For several years researchers have noticed that there appears to be a regular, year-by-year increase in the average IQ for the general population. This phenomenon is called the Flynn effect after the
In a classic study of infant attachment, Harlow (1959) placed infant monkeys in cages with two artificial surrogate mothers. One "mother" was made from bare wire mesh and contained a baby bottle from
Belsky, Weinraub, Owen, and Kelly (2001) reported on the effects of preschool childcare on the development of young children. One result suggests that children who spend more time away from their
Other research examining the effects of preschool childcare has found that children who spent time in day care, especially high-quality day care, perform better on math and language tests than
A random sample of n = 25 scores is obtained from a population with a mean of μ = 45. A treatment is administered to the individuals in the sample and, after treatment, the sample mean is M = 48. a.
A sample of n = 25 scores has a mean of M = 83 and a standard deviation of s = 15. a. Explain what is measured by the sample standard deviation. b. Compute the estimated standard error for the sample
A random sample is obtained from a population with a mean of μ = 70. A treatment is administered to the individuals in the sample and, after treatment, the sample mean is M = 78 with a standard
An example of the vertical-horizontal illusion is shown in the figure below. Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength
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