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applied statistics and multivariate
Straightforward Statistics With Excel 2nd Edition Chieh-Chen Bowen - Solutions
2. Beach resorts had annual reports on numbers of drowning accidents, ice cream sales, and numbers of visitors. Assume that the numbers of drowning accidents, ice cream sales, and visitors were all normally distributed. The Pearson’s correlation between drowning accidents and ice cream sales was
1. A group of 14 people was randomly selected and their cell phone bills and monthly income were reported in Table 10.6. Assume that income and cell phone bills are normally distributed.
4. Besides the regular normal distribution for the paired variables X and Y, there is an additional requirement called homoscedasticity.Try saying that 10 times in a row fast! Homoscedasticity is defined as the condition in which the variance of Y at any given value of X is the same across the
3. The scatterplot does not show obvious outliers. If outliers are attributed to data entry errors, remove those outliers before calculating correlations. The effect of other outliers can be identified by first calculating correlations with the outliers and calculating correlation again without
2. The scatterplot confirms the existence of a linear relationship between two variables.
1. Variables X and Y form a bivariate normal distribution, which means that X values are normally distributed, Y values are normally distributed, and for every value of X, Y values are normally distributed.
1. Both test–retest reliability and criterion-related validity can be calculated by 1. t tests.2. Z tests.3. F tests.4. Pearson’s r.2. The direction of Pearson’s r is determined by?
Describe how to purify the relationship between two primary variables by keeping the third variable constant using partial correlation?
Explain the coefficient of determination
Define and explain the purpose of Pearson’s product moment correlation, r Conduct a hypothesis test on Pearson’s r
3. Calculate and interpret the effect size of the difference in students’ average GPA between these two types of learning.
2. What is the 90% CI for the differences of GPA between these two types of learning?
1. Conduct a proper statistical procedure to test whether the types of learning have a significant effect on students’ GPA.
4. not be possible to determine based solely on the information provided here?
6. With α = .05 and df = 8, the rejection zone for a right-tailed t test is t > 1.860. Assuming that all other factors are held constant, if the df increases to 20, the critical value of t that sets the boundary for the rejection zone would 1. increase 2. decrease 3. remain the same
5. When the correct formula for calculating the effect size for the independent-samples t test is 1. Cohen’s d 2. Satterthwaite’s df 3. the folded F test 4. Glass’s Δ
4. When the correct df for the independent-samples t test is 1. df = df1 + df2 2. Satterthwaite’s df 3. df = n1 + n2 − 1 4. df = n1 + n2?
3. When the correct formula for calculating the effect size for the independent-samples t test is 1. Cohen’s d 2. Satterthwaite’s df 3. the folded F test 4. Glass’s Δ?
4. pool the means together?
2. When the correct procedure to compare means is to 1. pool the variances together 2. pool the degrees of freedom together 3. leave the variances the way they are when calculating the standard error of the mean difference
4. When equal variances are not assumed?1. The folded F test, is a test for 1. equality of means 2. equality of variances 3. equality of correlations 4. equality of probabilities?
3. When two samples are randomly selected from two populations
2. When equal variances are assumed
1. When two samples are carefully matched on the group means.
4. (r − 1)(c − 1), where r is the number of rows and c the number of columns?1. The observations from the two samples must be independent.2. The number of groups needs to be two.3. Two samples are randomly selected from two populations.4. The two samples have equal variances.
2. Which degrees of freedom determine the critical values of an F test when conducting a test for equality of variances?1. n 2. n − 1 3. df1 for the numerator and df2 for the denominator
1. The F statistic to test the equality of variances specifies the larger variance as the numerator and the smaller variance as the denominator. Such a process is called a folded F test; therefore, the critical values listed in the F Table are 1. positive and greater than 1.2. left-tailed values.3.
Describe the roles of Cohen’s d and Glass’s delta (Δ) in calculating the effect sizes of the independent-samples t tests?
Calculate and interpret confidence intervals
Describe the five-step hypothesis procedure for independent-samples t tests
Explain the purpose for the test of the equality of variances
Describe the decision rules for equal variances assumed versus equal variances not assumed
Define the independent-samples t test and explain when it can be properly used
11. A researcher is conducting a study to evaluate a program that claims to increase short-term memory capacity. The short-term memory capacity score is normally distributed with µ = 7. Both theoretical reasoning and previous empirical research have shown a strong positive effect of this kind of
10. A Type I error means that a researcher has 1. rejected the null hypothesis (H0) when H0 is actually true 2. rejected the null hypothesis (H0) when H0 is actually false 3. accepted the null hypothesis (H0) when H0 is actually true 4. accepted the null hypothesis (H0) when H0 is actually false
9. The starting point of a hypothesis test is the null hypothesis, which 1. states that the effect does not exist 2. is denoted as H1 3. is always stated in terms of sample statistics 4. states that the effect exists
8. For a two-tailed test with α = .01, the critical values that set the boundaries for the rejection zones are 1. Z > 1.96 2. Z > 2.58 3. |Z| > 1.96 4. |Z| > 2.58
7. Type I error means that a researcher has 1. claimed a treatment effect when the effect actually exists 2. claimed a treatment effect when the effect actually does not exist 3. failed to claim a treatment effect when the effect actually exists 4. failed to claim a treatment effect when the effect
6. In a one-tailed test, H0: µ = 10, H1: µ > 10, the rejection zone is 1. on the right tail of the distribution 2. on the left tail of the distribution 3. in the middle of the distribution 4. evenly split into two tails
5. Putting innocent people in jail is analogous to falsely claiming a research effect when the effect does not exist. Both are __________ errors.1. Type I 2. Type II 3. Type III 4. Type IV
4. In a one-tailed test, H0: µ = 120, H1: µ < 120, the rejection zone is 1. on the right tail of the distribution 2. on the left tail of the distribution 3. in the middle of the distribution 4. evenly split into two tails
4. fail to claim a treatment effect when the effect does not exist 3. A normal adult population is known to have a mean µ = 65 on the WPA cognitive ability test. A higher score means better cognitive ability. A researcher studied the detrimental effects of chemotherapy on brain function, so she
3. fail to claim a treatment effect when the effect actually exists
4. fail to reject the null hypothesis (H0) when H0 is actually false 2. A Type II error refers to 1. claim a treatment effect when the effect actually exists 2. claim a treatment effect when the effect actually does not exist
3. fail to reject the null hypothesis (H0) when H0 is actually true
2. reject the null hypothesis (H0) when H0 is actually false
1. The statistical power refers to the sensitivity to 1. reject the null hypothesis (H0) when H0 is actually true
3. A car manufacturer claims that a new model Q has an average fuel efficiency µ = 35 miles per gallon on the highway, and a standard deviation σ = 5. The American Automobile Association randomly selected 40 new Qs and measured their fuel efficiency at 33 miles per gallon. Was the car
2. The expenditure per pupil for K–12 public schools in the United States has a normal distribution with a mean µ = $12,611.84 and a standard deviation σ = $4,148.46. Researchers randomly selected a group of 50 high performing public schools, and their average expenditure per pupil was
1. According to the ACT Profile Report—National, the ACT composite scores are normally distributed with µ = 21.0 and σ =5.4. Many charter schools received funding from the state government without providing accountability measures as required by the public schools. A sample of 36 high school
6. When exploratory research is conducted without extensive prior research or theoretical reasoning to suggest a particular direction of relationship, the preferred hypothesis tests should be __________.1. two-tailed tests 2. one-tailed tests 3. whichever is easier to produce significant results 4.
5. For a two-tailed Z test with α = .10, the critical values that set the boundaries for the rejection zones are 1. Z > 1.65 2. Z > 1.96 3. |Z| > 1.65 4. |Z| > 1.96
4. What values are needed to figure out the rejection zones for Z tests?1. The α level 2. One-tailed test or two-tailed test 3. Sample size 4. Both (a) and (b)5. All of the above
3. Which of the following variables is positively correlated with the statistical power?1. The probability of committing a Type I error, α2. The sample size, n?3. The effect size 4. All of the above three variables are positively correlated with the statistical power.
2. What is the correct definition of Type II error?1. Reject H0 when H0 is true.2. Fail to reject H0 when H0 is true.3. Reject H0 when H0 is false.4. Fail to reject H0 when H0 is false.
1. What is the correct definition of Type I error?1. Reject H0 when H0 is true.2. Fail to reject H0 when H0 is true.3. Reject H0 when H0 is false.4. Fail to reject H0 when H0 is false.
Explain why rejecting a null hypothesis or failing to reject a null hypothesis are mutually exclusive and collectively exhaustive?
Describe the relationship between the α level and the rejection zone when conducting a hypothesis test
Compare and contrast a one-tailed test and a two-tailed test
Explain the importance of the null hypothesis and the alternative hypothesis in conducting a hypothesis test
Identify and describe the four steps in conducting a hypothesis test
Define the terms Type I error and Type II error, and explain their meanings in hypothesis tests
14. A food processing company labels the net weight of a bag of frozen chicken vegetable dumplings as µ = 16 ounces. According to the company’s records, the standard deviation of the net weights of the frozen chicken vegetable dumplings is σ = 1.5 ounces. What is the probability of randomly
13. An internet car insurance company advertises that it takes µ =15 minutes to get an insurance quote to save you money. The company’s records show that the standard deviation for the time spent on the site to get insurance is σ = 5 minutes. The company randomly selects a sample of 16
12. A new water taxi has a maximal load capacity of 3,200 pounds. Adult males’ weight is normally distributed with µ = 182.5 pounds and σ = 40.8 pounds and adult females’ weight is normally distributed with µ = 165.2 pounds and σ = 45.6 pounds.The safety certificate sets the maximum number
11. What are the Z values that set the middle 99% apart from the rest of the distribution?
10. A sample is obtained from a population with µ = 100 and σ = 10.Which of the following sample means would produce a Z score closest to zero?
9. A random sample of n = 14 scores is obtained from a normal population with µ = 19.87 and σ = 4.12. What is the probability of randomly selecting a sample with a mean less than 21?1. .1587 2. .3085
8. Which of the following samples would have the smallest standard error of the mean?1. n = 25 from a population with σ = 10 2. n = 25 from a population with σ = 20 3. n = 100 from a population with σ = 10 4. n = 100 from a population with σ = 20
7. A population is normally distributed with µ = 80 and σ = 8. The sampling distribution of sample means for sample size n = 4 selected from this population would have a standard error of the mean of __________.1. 80 2. 8 3. 4 4. 2
6. The number of days of hospital stay after a particular procedure is a skewed distribution. Researchers randomly select 40 patients after this procedure. Assuming that the sampling process can be repeated many times, the shape of the sampling distribution of sample means is 1. the same shape as
5. What is the probability of randomly selecting a sample of n = 20 people with an average happiness score greater than 60?Assume that happiness scores are normally distributed with a µ =65 and σ = 15?1. .0681 2. .0823 3. .9177 4. .9319
4. The standard deviation of all sample means is also called 1. the standard error of the mean 2. the sampling error 3. the central limit theorem 4. the sum of squared deviations
3. In any normal distribution, the middle 50% is bound by __________.1. −0.5 < Z < 0.5 2. −0.67 < Z < 0.67
2. Assume that adult heights forms a normal distribution with a mean, µ = 68.34 inches and a standard deviation, σ = 6.57 inches. What is the probability of randomly selecting a group of 25 people and their average height is taller than 5 feet 11 inches?1. .9783 2. .9772 3. .0228 4. .0217
1. Assume that IQ test scores are normally distributed with a mean of 100 and standard deviation of 10. What is the probability of randomly selecting an individual with an IQ greater than 130?1. .9987 2. .0013 3. .9772 4. .0228
3. The Logistics Director of a company that manufactures personal protective equipment (PPE) tries to figure out the probability of fitting 110 boxes of PPEs into a small cargo plane to expedite the shipping so hospitals can receive?
2. The SAT ERW score is normally distributed with µ = 497 and σ =115. What is the probability of randomly selecting a group of 25 high school seniors to obtain their average SAT ERW score less than 450?
3. Explain the impact of sample size on the results.
2. What is the probability of randomly selecting a group of 50 teenagers whose average screen time is greater than 3.5 hours?
1. What is the probability of randomly selecting a group of five teenagers whose average screen time is greater than 3.5 hours?
1. Assume teenagers’ screen time is normally distributed with a mean µ = 3.2 hours and a standard deviation σ = 1.1.
4. The law of large numbers describes the relationship between the sample means and the population mean as which of the following numbers approaches infinity?1. The number of successes 2. The population mean 3. The number of trials 4. The sample mean
4. When samples of a particular sample size, n ≤ 30, are randomly selected from a population that is not normally distributed.
3. When samples of a particular sample size, n ≤ 30, are randomly selected from a normally distributed population.
2. When samples of a particular sample size, n > 30, are randomly selected from a population that is not normally distributed.
1. When samples of a particular sample size, n > 30, are randomly selected from a normally distributed population.
3. What is the standard error of the mean for a sample size of 100?
2. What is the standard error of the mean for a sample size of 25?
1. What is the standard error of the mean for a sample size of 4?
4. The standard error of the mean is the standard deviation of all sample means,
3. The mean of all sample means (also called the expected value of the mean) is the population mean,
2. If the population is normally distributed, the sampling distribution of the sample mean is also normally distributed regardless of the sample size.
1. The sampling distribution of the sample means becomes more and more normally distributed as the sample size increases.When sample size n > 30, the sampling distribution of means is approximately normally distributed regardless of the shape of the original population distribution.
4. University students were assigned a number; then, 10% of the students were selected by a random number generator to provide opinions on the campus parking services.
3. The ratings collected by ratemyprofessors.com.
2. Pollsters asked voters how they cast their ballots at the exit of a voting location.
1. TV shows asked the audience to call in to vote for their favorite contestants.
1. Which one of the following sampling procedures makes an effort to minimize nonsampling errors?
Describe how a Z test is conducted, and interpret the results of a Z test?
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