Chapter 11 Statistics

For x̅=125, s∨x=10, N=26, and µ=128, t-obt=____ and t-crit=____ for a one-tailed test with Ha: µ>128 and α=0.01. A. -1.530; 2.485 B. -1.530; -2.485 C. -2.485; 1.530 D. -2.485; -1.530

A

For x̅=52, s∨x=3, N=20, and µ=50, t-obt=____ and t-crit=____ for a two-tailed test with α=0.05. A. 2.981; 2.093 B. 2.093; 2.981 C. -2.981; -2.093 D. -2.093; -2.981

A

What does the shape of any particular sampling distribution of a correlation coefficient depend upon? A. df B. µ C. r D. r²

A

If a researcher reports a one-sample t-test with df=24, how many individuals participated in this study? A. 24 B. 25 C. 26 D. Cannot be determined from the information given

B

What does the t∨obt value indicate? A. The probability of rejecting the null hypothesis B. The probability of retaining the null hypothesis C. How far the population mean, µ, is from the mean of the sampling distribution of means D. How far the sample mean is from the µ of the sampling distribution in estimated standard error units

D

What is the difference between Pearson's and Spearman's correlations when performing a hypothesis test? A. The level of α B. The size of the sample C. The assumption that the scores must be randomly selected D. How the respective sampling distributions for each correlation are conceptualized

D

When is a t-test used instead of a z-test? A. When the population µ is known B. When the population deals with two samples C. When the population standard deviation is known D. When the population standard deviation is unknown

D

If all other factors are held constant, increasing the level of confidence will have what kind of effect on the width of a confidence interval? A. Increase it B. Decrease it C. Increase it or decrease it depending on whether t-obt is positive or negative D. Have no effect on it

A

In a one-tailed significance test for a correlation predicted to be negative, the null hypothesis is ______ and the alternative hypothesis is ______. A. H₀: p≥0; Ha: p<0 B. H₀: p>0; Ha: p≤0 C. H₀: p=0; Ha: p<0 D. H₀: p>0; Ha: p<0

A

In a one-tailed significance test for a correlation predicted to be positive, the null hypothesis is _____ and the alternative hypothesis is _____. A. H₀: p≤0; Ha: p>0 B. H₀: p<0; Ha: p≥0 C. H₀: p=0; Ha: p>0 D. H₀: p<0; Ha: p>0

A

Some people claim that psychology is common sense. If this is truee, then students who have not taken psychology courses should be able to predict the outcomes of experiments as well as psychology majors. If it is not, nonpsychology students should perform worse than psychology students. Psychology students typically predict outcomes with µ=75% accuracy. A sample of 15 nonpsychology students predicted with x̅=60% accuracy. The s∨x=2.696. What is the 95% confidence interval for nonpsychology students? A. 54.22≤µ≤65.78 B. 54.26≤µ≤65.75 C. 55.25≤µ≤64.75 D. 69.22≤µ≤80.78

A

The alternative hypothesis in a two-tailed significance test of correlation states that A. a correlation exists in the population B. no correlation exists in the population C. a positive correlation exists in the population D. a negative correlation exists in the population

A

The process of specifying a range of values within which the population parameter is estimated to fall is known as A. Interval estimation B. Mean estimation C. Point estimation D. Population estimation

A

What happens to the absolute value of t-crit as df increases? It A. decreases B. increases C. remains the same D. increases or decreases depending on whether t-obt is positive or negative

A

When establishing the proper confidence interval for interval estimation, which of the following should be employed? A. A two-tailed value of t-crit B. A one-tailed value of t-crit C. A one-tailed value of t-obt D. A two-tailed value of t-obt

A

Which of the following statements about the correlation coefficient is true? A. One should not accept that a correlation coefficient represents a relationship unless it is significant B. Unless a correlation coefficient is zero, it represents a relationship C. Positive correlation coefficients tend to be significant more often than negative ones D. Sampling error does not apply to the correlation coefficient

A

How many degrees of freedom do we have in significance testing of r? A. N-2, where N equals the total number of Xs plus the total number of Ys B. N-2, where N equals the total number of pairs of scores C. N-1, where N equals the total number of pairs of scores D. N-1, where N equals the total number of Xs plus the total number of Ys

B

If a sample mean has a value equal to µ, the corresponding value of t will be equal to A. +1.0 B. 0.0 C. -1.0 D. +2.0

B

In a study involving 22 participants, you have found that the Pearson correlation coefficient between the amount of Chemical J2 and roller coaster enjoyment is 0.53. Use a two-tailed test and α=0.01 to determine if this is a significant correlation coefficient. A. r-crit=0.413, p<0.05 B. r-crit=0.537, p>0.05 C. r-crit=0.423, p<0.05 D. r-crit=0.537, p<0.05

B

The Cultural Diversity Task Force sponsored six events last year (e.g., Awareness Luncheon) and six events with the same names this year. To see how well the attendance last correlated with the attendance this year, the chairperson ranked the number of people attending each event during each of the two years and calculated a correlation. The chairperson used the Spearman rank-order correlation coefficient (α=0.05) to determine if attendance this year at these events was greater than last year (a positive correlation). The correlation would have to be bigger than ______ to be "significant." A. 0.886 B. 0.829 C. 0.645 D. 0.643

B

The critical value for r is obtained using A. N, which is the total number of scores in the sample B. N, which is the number of pairs of scores in the sample C. df, which equals N-1, with N being the number of pairs of scores in the sample D. df, which equals N-2, with N being the number of pairs of scores in the sample

B

The logic behind computing a confidence interval is to compute the highest and lowest values of a _____ mean that are not significantly different from those of _____. A. sample; the current sample mean B. population; the current sample mean C. population; the population mean specified in the null hypothesis D. sample; the population mean specified in the null hypothesis

B

The null hypothesis in a two-tailed significance test of correlation states that A. a correlation exists in the population B. no correlation exists in the population C. a positive correlation exists in the population D. a negative correlation exists in the population

B

What happens to the power of a t-test when the variability of the raw scores is increased? The power will A. increase B. decrease C. remain the same D. increase or decrease, depending on whether t-obt is positive or negative

B

What happens to the t-distribution as the sample size increases? A. The t-distribution appears less and less like a normal distribution B. The t-distribution appears more and more like a normal distribution C. The shape of the t-distribution is unaffected D. s∨x̅ becomes nearer to the true value of µ

B

What is t-crit for a one-tailed negative test when 30 participants are tested? Use α=0.05 A. -1.697 B. -1.699 C. ±2.042 D. ±2.045

B

When we construct a 95% confidence interval, we are 95% sure that the A. sample mean falls within the interval B. population mean falls within the interval C. sample mean is at the center of the interval D. population mean is at the center of the interval

B

Which of the following is one of the assumptions for hypothesis testing of the Pearson correlation coefficient? A. The X-Y pairs are ordinal scores B. There is random sampling of X-Y pairs C. The dependent variable comes from a population that has a normal distribution D. The independent variable comes from a population that has a normal distribution

B

Which of the following is one of the assumptions of a one-sample test? A. The obtained scores are on an ordinal or interval scale B. The population standard deviation is estimated by computing s∨x C. The population standard deviation is known D. The population distribution is skewed

B

A developmental psychologist interested in the development of color perception presented 20 one-month-old infants with a pair of color forms. One form had two colors and the other hand had one. If the infants preferred to look at the form with two colors above chance level (50%), they can perceive colors. The mean percentage of times the infants preferred the two-color form was 53.15 (s²x=14.345). What is t-obt? A. 0.83 B. 0.98 C. 3.72 D. 4.39

C

A study with 46 participants investigated whether there was a relationship between one's attitude toward giving blood and the number of times one has given blood in a year. The correlation coefficient was r=+0.56. The r-crit is _____ and the investigator should _____. A. +0.243; reject H₀ B. +0.243; retain H₀ C. ±0.243: reject H₀ D. ±0.243: retain H₀

C

Degrees of freedom (df) for the one-sample t-test is equal to A. √N B. N C. N-1 D. s∨x̅

C

For x̅=7, s∨x=11, N=15, and µ=91, what is t-obt? A. t(14)=0.27 B. t(14)=0.36 C. t(14)=-1.41 D. t(14)=-3.95

C

How is the t-distribution defined? A. The distribution of all possible values of t B. How far the sample mean is from the µ of the sampling distribution in estimated standard error units C. The distribution of all possible values of t for random sample having the same N from the population described by H₀ D. The distribution of all possible values of t for random sample having the same N from the population described by Ha

C

If r=0.72, what proportion of the variance in Y is accounted for by its relationship with X? A. 0.85 B. 0.72 C. 0.52 D. Cannot be determined from the information given

C

If we reject the null hypothesis in a significant test of correlation, we conclude that there is A. a significant difference between the sample correlation coefficient and the true value of p B. a significant difference between the sample mean and the true population mean C. a nonchance relationship between the X and Y variables D. a chance relationship between the X and Y variables

C

In a study involving 22 participants, you have found that the Pearson correlation coefficient between the amount of Chemical J2 in the bloodstream and roller coaster enjoyment is 0.53. Use a two-tailed test and α=0.05 to determine if this is a significant correlation coefficient. A. r-crit=0.413, p<0.05 B. r-crit=0.537, p>0.05 C. r-crit=0.423, p<0.05 D. r-crit=0.404, p<0.05

C

The confidence interval for a single µ is A. a point interval estimation of the population mean B. an interval containing values of µ that our sample mean is not likely to represent C. an interval containing values of µ that our sample mean is likely to represent D. a point on the variable at which the population µ is expected to fall

C

The major problem with point estimation is that it A. cannot be utilized to estimate population parameters B. cannot be utilized with sample data C. is extremely vulnerable to sampling error D. provides only a single point in its estimate

C

What is s∨x̅? A. The estimated population standard deviaiton B. The population standard deviation C. The estimated standard error of the mean D. The standard error of the mean

C

What is the purpose of using a confidence interval? A. to estimate the value of a sample mean B. to use a level of confidence to estimate a sample mean C. to use a sample mean to estimate the value of a population mean D. to use the sample mean to determine the population level of confidence

C

Which kind of estimation is performed when we claim that a population mean is equal to the sample mean? A. Interval estimation B. Mean estimation C. Point estimation D. Population estimation

C

Which of the following would increase the power of a significance test for correlation? A. Changing α from 0.05 to 0.01 B. Increasing the variability in the Y scores C. Changing the sample size from N=25 to N=100 D. Changing the sample size from N=100 to N=25

C

Which of the following would increase the power of a t-test? A. Changing α from 0.05 to 0.01 B. Increasing the variability in the raw scores C. Changing the sample size from N=25 to N=100 D. Changing the sample size from N=100 to N=25

C

A two-tailed t-test was conducted for x̅=97, s∨x=10, N=14, and µ=94. Using α=0.05, t-crit=2.160 was compared to t-obt. What is the correct 95% confidence interval for µ? A. 75.40≤µ≤118.60 B. 85.80≤µ≤108.20 C. 72.40≤µ≤115.60 D. A confidence interval should not be constructed because the t-test was not significant

D

A two-tailed t-test was conducted for x̅=97, s∨x=5, N=21, and µ=100. Using α=0.05, t-crit=2.086 was compared to t-obt. What is the correct 95% confidence interval for µ? A. 86.57≤µ≤107.43 B. 83.25≤µ≤110.75 C. 89.57≤µ≤110.43 D. A confidence interval should not be constructed because the t-test was not significant.

D

For a two-tailed test with α=0.05, the t-crit value is A. either +1.96 or -1.96 B. both +1.96 or -1.96 C. either +1.645 or -1.645 D. different for each df

D

Suppose you conduct an experiment with 20 subjects and t-obt turns out to be 0.69, which is not statistically significant. Which of the following is the correct way to report your results? A. t-obt=0.69, p>0.05 B. t(20)=0.69, p<0.05 C. t(19)=0.69, p<0.05 D. t(19)=0.69, p>0.05

D

Suppose you conduct an experiment with 24 subjects and your t-obt turns out to be 2.92, which is statistically significant. Which of the following is the correct way to report your results? A. t-obt=2.92, p<0.05 B. t(24)=2.92, p<0.05 C. t(23)=2.92, p>0.05 D. t(23)=2.92, p<0.05

D

Suppose you correlate reading levels with the ages of 30 elementary school children. You compute r-obt and find it to be 0.72, which is a significant correlation coefficient. Which of the following is the most appropriate conclusion? A. Increases in age cause increases in reading level B. There is a proven relationship between age and reading level C. There is a negative relationship between age and reading level that exceeds chance expectations D. There is a positive relationship between age and reading level that exceeds chance expectations

D

Suppose you perform a two-tailed significance test on a correlation between the number of books read for enjoyment and the number of credit hours taken, using 32 participants. Your r-obt is -0.15, which is not a significant correlation coefficient. Which of the following is the correct way to report this finding? A. r(32)=-0.15, p>0.05 B. r(31)=-0.15, p>0.05 C. r(30)=-0.15, p<0.05 D. r(30)=-0.15, p>0.05

D

Suppose you perform a two-tailed significance test on a correlation using 29 participants. Your r-obt is 0.56, which is a significant correlation coefficient. Which of the following is the correct way to report this finding? A. r(29)=0.56, p<0.05 B. r(28)=0.56, p<0.05 C. r(27)=0.56, p>0.05 D. r(27)=0.56, p<0.05

D

Unless we use the correct t-crit from the t-distribution for the appropriate N, A. we will fail to reject H₀ B. we will always reject H₀ C. the probability of making a Type I error will increase D. the probability of making a Type I error will not equal α

D

Which of the following assumptions is common to both the z-test and the one-sample t-test? A. Alpha is selected to be 0.01 B. The raw score population forms a normal distribution, and the population mean and standard deviation are known C. The standard deviation of the raw score population is estimated by s∨x D. There is one random sample of interval or ratio scores

D