Stat exam 1
Suppose the correlation coefficient between the height and weight for adults is +0.60, what proportion (or percent) of the variability in the weight is due to the relationship with the height?
60%
For a statistics quiz of 100 students, the 40th percentile is 80, which statement is Correct?
60% of students scores exceed 80
What is the percentile rank of the score of 80 on the psychological test with the mean of 60 and standard deviation of 20 in a normal distribution?
84.13
True or False: If the percentile rank of a score is 78 is 60, we can say that 60% of the scores fall below 78. Explain:
True, because in order to get the percentile, we calculate the scores under which the distributed percentile lies.
What it the Type I error? What is the type II error?
Type 1: We reject the null hypothesis that the mean score is 65 but actually the mean score is 65. Type 2: We did not reject the null hypothesis that mean score is 65 but actually it is not 65.
4. What is the possible type I error? what is the type II error?
Type 1: we rejected the hypothesis that there is no difference in the performance, when actually there is NO difference in the performance Type two: accept the null when it is wrong
In an One-sample T test, the significance level is 0.05. The calculated t test statistics is -1.069 and its P-value is 0.06, which statement is correct?
We fail to reject the null hypothesis the same logic as the last problem. If P value is greater than Significance level, we will not reject Null Hypothesis
Is the population mean difference within the 95% Confidence Interval of the Difference?
Yes
1. What is the percentile rank of a standardized normal score of −2.0? a) About 2nd b) About 34th c) About 50th d) About 98th
a) About 2nd
_________Which scale of measurement is produced by the following survey item: "Which season is your favorite, spring, summer, fall, or winter?" a) Nominal b) Ordinal c) Interval d) Ratio
a) Nominal
Which of the following is an example of a Nominal measurement scale?
the hair color
Adding just one or two extreme scores to the high end of a large distribution of scores will have a greater effect on:
the median than on the mode.
The variance and standard deviation are affected by extreme scores
true
A researcher tested the hypothesized equality of two population means with a two-tailed test using computer software. The reported p-value was .06 and she had the significance level at .05. She should:
Fail to reject the null hypothesis If P value is greater than significance level/alpha level, we will Not reject the null Hypothesis. P value is large, it means that the sample is NOT an unlikely event. When a likely event occur, we will not have strong evidence to reject Null hypothesis
Bar graphs are used to illustrate the data when the scale of measurement of the the variable is interval
False
If the percentile rank of a score of 80 is 65, we can say that 65% of the scores exceed 80.
False
Suppose that a psychologist is interested in performance on a task under sleep-deprived conditions versus rested conditions, as measured by the number of errors made on the task. This researcher, who predicts that more mistakes will be made in the sleep-deprived condition, set alpha (significance level) =0.01. 1. How many groups are involved in this study?
2 groups
1) How many scores lies between 45 and 100?
2=0.97 -0.75= 0.22 0.97-0.22=0.75 75% of the scores are between 45 and 100
For a standard normal distribution, the area between z=-1 and Z=0 is 0.3413, which following statement is Correct?
34.13 percent of the test scores between Z=-1 and Z=0
Which is the weakest correlation coefficient?
+0.07
2. What is the T-test value?
-0.140
Which one is the strongest correlation?
-0.89 the closer to 1 or -1, the stronger
Which of the following correlation coefficients, each obtained from a sample of 1000 children, indicates the strongest relationship?
-0.9
Which of the following are more likely to lead to the rejection of the null hypothesis?
0.05
What is the weakest correlation?
0.06
The proportion of scores in a normal distribution that corresponds to a z-score greater than +1.04 is approximately___? (Hints, use table A 1, find the area on the right size of Z=+1.04)
0.1492
1) How many scores are less than the score of 45?
0.773 , 77% 25% of the scores less than 45
1. A student came home with two test scores, z = +1 in math and z = −1 in biology. Answer the following questions: 1) What is the percentile rank for the math score z=1? (Use the Table A.1) 2) What is the percentile rank for the biology score z=-1? 3) Which score is above the mean? which one is below the mean? Explain
1) 84% 2) 15% 3) Math is above the mean because it is a positive value, and biology is below the mean because it is a negative value.
1) How many scores exceed the score of 100?
1-0.97 = 0.03 3% of the scores exceeded 100
Assume that a set of 300 scores in normally distributed with a mean of 60 and a standard deviation (SD) of 20 1) What are the Z scores corresponding to the raw scores of 100, 60, and 45?
100-60/20= 2 60-60/20= 0 45-60/20= -0.75
1) Find the percentile ranks of the score of 100, 60, and 45.
97% , 50% , 25%
Assume that there is a general tendency for people who watch less TV to have lower blood cholesterol. Which finding is most likely?
A researcher obtained a correlation of r = +0.62 between the amount of time spent watching TV and the level of blood cholesterol
Assume that is a general tendency for students who spend more time on study to have higher GPA, which finding is most likely?
A researcher obtained a correlation r=0.6 between the amount of time spent on study and GPA
1. If in a distribution of 100 IQ scores, the mean is considerably less than the median, then the distribution is which of the following? a) Negatively skewed b) Symmetrical c) Positively skewed
A) Negatively skewed Explain: The data is distributed on the right of the median is greater than the left of the median which means that the mean is less than the median.
1. Which of the following represents the highest performance in a standard normal distribution? a) P90 (means 90 percentile) b) z = +1.00 c) Q3 d) P70 (means 70 percentile)
A) P90 (means 90 percentile) Explain: it is the highest because 90% of the values fall under it.
If all residents of Pennsylvania (PA) make up a population, which one is mostly likely NOT a sample of this population. (We used the Webster definition for residents for this problem: a person living in a place for some length of time)
All students of Widener University
Step Two: Set the criterion for Rejecting the Null. (read textbook) What is the significance level (alpha) that you select for this study before you perform the statistical analysis?
Alpha is set at 0.05
Step Two: Set the criterion for Rejecting the Null. (read textbook) What is the significance level (alpha) that you select for this study before you perform the statistical analysis?
Alpha set at 0.05
What is the alternative hypothesis for this study Ha:
Alternative Hypothesis: The special training in reading skills resulted in change, that is, the mean score is NOT 65
The null hypothesis is a statement about which of the following?
An unknown parameter Because we are making a hypothesis about whether a thing is supported or not and make an interference about two possibilities regarding a population. And because it is unknown, it might lead to a right or wrong decision regarding a population.
Data have been collected on how often adults feel they "eat healthy" during an average week. Responses include: "all the time," "most of the time," "sometimes," and "never." Which of the following graphs would be appropriate to use to graph this variable? Select all that apply
Bar graph
1. A physical education teacher is conducting research related to elementary children's time spent in physical activity. As part of his research, he collects data from schools related to the number of minutes that they require children to participate in physical education classes. She finds that the most frequently occurring number of minutes required for children to participate in physical education classes is 22.00 minutes. Which measure of central tendency does this statement represent? a) Mean b) Median c) Mode d) Range e) Standard deviation
C) mode Explain: The mode is the number that occurs most frequently in a set of numbers.
The statics professor wants to investigate the Widener students' test anxieties. The professor obtained a list of all classes in the Fall, 2017 and randomly selected 10 classes, what sampling method did the professor use?
Cluster Sample
Selecting classrooms of students and then using all the students in each classroom selected, is an example of
Cluster sampling In this case, the whole classroom is the unit not the individual student. It is a typical cluster sampling
What is the regression coefficient in the equation? What is the regression constant in the equation?
Coefficient R = 0.88 Constant B = 31
A mental health counselor is conducting a research study on satisfaction that married couples have with their marriage. In this scenario, "Marital status" (e.g., single, married, divorced, widowed) is which of the following? a. Constant b. Variable
Constant
What is the alternative hypothesis for this study Ha:
Exam scores are not μ = 42
An instructor has been teaching large sections of general psychology for the last 10 semesters. As a group, final exam scores are normally distributed with μ = 42 and σ = 10. With the current class of n = 100, the instructor tries a different teaching format. Once a week, the class breaks down into smaller groups that meet with the instructor for discussion of recent lecture and reading material. At the end of the semester, the instructor notes that the mean for his section on the final exam was X = 46.5. Did the teaching format have a significant effect on performance on the final exam? Test with alpha set at .05. 1. Step One: State the Null Hypothesis
Exam scores are μ = 42
Step Three: Compute the Test Statistic What is the Test statistic that you will use to test the null Hypothesis? Show the process that how did you compute the Test statistic
First compute the standard error of the mean: 10/the root of 100 = 1 Then compute the test statistic z: Z= 46-42/1 =4.5
3 Step Three: Compute the Test Statistic What is the Test statistic that you will use to test the null Hypothesis? Show the process that how did you compute the Test statistic
First compute the standard error of the mean: 5/ the root of 25= 1 Then compute the test statistic z: Z= 16-18/1 = -2
An elementary school principal correlated the reading comprehension scores and the mathematics concept scores from a test, which correlation was probably the highest?
For all children between grades 2 and 6 the less homogenous or the more variability, the Higher correlation In this case, children from grade 2 to 6 is the most diverse group compared to others, so we can see the highest correlation coefficient
Which correlation was probably the lowest, explain?
For all third graders with vocabulary scores above the school mean, because he restricted the variables, and it is more homogenous.
Which following sample is a simple random sample?
In a health clinic, all patients were assigned a identification number, and a computer generated a list of random numbers. Members are included in the sample if their identification numbers are on the list of random numbers Each eligible member has the equal chance to be selected
Which of the following is true of the variance of a distribution of scores?
It can be any number equal to or greater than zero.
What amount of variability in "Income" was explained by the years of experiences? (Look at the table 1, R square tells the amount of variability being explained
It explains about 76.3% of the variability in income.
Kathy's percentile rank on a science test was 46, which means:
Kathy equaled or surpassed 46% of the test takers
A physical education teacher is conducting research related to elementary children's time spent in physical activity. As part of his research, he collects data from schools related to the number of minutes that they require children to participate in physical education classes. She finds that the most frequently occurring number of minutes required for children to participate in physical education classes is 22.00 minutes. Which measure of central tendency does this statement represent?
Mode
2. State the null and alternative hypothesis:
No mistakes will be made under the two different conditions
A researcher begins with a known population whose scores on a standardized test are normally distributed with μ = 65 and σ = 15. The researcher suspects that special training in reading skills will produce a change in the scores for the individuals in the population. Because it is not feasible to administer the treatment (the special training) to everyone in the population, a sample of n = 25 individuals is selected, and the treatment is given to this sample. Following treatment, the average score for this sample is = 75. This study is to find out whether there is evidence that the training has an effect on test scores for the population, for this assignment, you are to answer the following questions: 1. State the Hypothesis
Null Hypothesis: The special training in reading skills resulted in NO change, that is, the mean score is still 65
The statement that there is no relationship or no difference is called
Null hypothesis Null hypothesis is always NO difference or NO effects
Using letter grades (A, B, C, D, F) to classify student performance on an exam is an example of measurement on a(n) _____ scale of measurement.
Ordinal
Identify the measurement scale for each of the following (Nominal, Ordinal, Interval or ratio)
Ratio A) Number of children in families Ordinal B) Grading system (A, B, C, D, F) Interval C) Level of blood sugar Nominal D) Gender Ratio E) Amount of gasoline consumed Nominal F) Majors in college Interval G) temperature
The regression equation ŷ=bX+a, where ŷ is _____
The predicted score
A type I error occurred when
Reject the null hypothesis when it is Actually true
Do you reject the Null Hypothesis? that is, is there evidence to suggest that males and females differ significantly in their levels of daily caloric intake (using an alpha level of .05)? How do you know?
Seeing how the P value is greater than 0.05, we fail to reject the null hypothesis
The Dean of the Nursing school at Widener is interested in the Junior nursing students' opinions on their field experience. She obtains a list of all Junior Nursing students and randomly selected 50 students to ask their opinions, which type of sampling method did she use?
Simple random sample
5. If the calculated P value is 0.05, do you reject or support the null hypothesis? Explain
Since it is greater than the alpha value then we will support the null hypothesis.
What is your decision about the null hypothesis? There are two possible decisions based on the step 3 results. Justify your decisions.
Since the alpha is 0.05 we divide it by 2 and that equals 0.025 which corresponds with +1.96 and -1.96. The Z score is 4.5 and it falls into the upper tail of the critical region. And since the score is very far from the critical region, the decision would be to reject the null hypothesis.
4. What is your decision about the null hypothesis? There are two possible decisions based on the step 3 results. Justify your decisions.
Since the alpha is 0.05, we divide it by 2 and that equals 0.025 which corresponds with +1.96 and -1.96. The Z test statistic value falls under the tail of the critical region and just slightly under -1.96. my decision is to reject the null hypothesis
A Z-score of Z= -0.25 indicates a location that is:
Slightly below the mean
If you want to assess presidential candidate preferences of Delaware County registered voters classified by social class and age, you might randomly select voters from each subgroup according to their proportion in the entire county. This sampling technique is called ________ sampling.
Stratified
3. What statistical test would you use? Why? (Did you use Z-test statistics or T test statistics, why?)
T-test score because there are two group
In the regression equation ŷ=bX+a, the value for the slope (b) indicates
The absolute value of the correlation coefficient
The larger the correlation coefficient
The better the prediction accuracy and the smaller the standard errors of estimate The higher correlation, means the variable have a stronger relationship with the dependent variable, therefore, it is more accurately to predict the dependent variable
An elementary school principal correlated the reading comprehension scores and the mathematics concepts scores from a standardized achievement test (1) For all children between grade 1 and 5. (2) For all third graders, and (3) For all third graders with vocabulary scores above the school mean. 1) Which correlation was probably the highest, explain?
The correlation for all children between 1 and 5, because the older the children ALL others same(such as same number of subjects etc), increasingly homogenous, the correlation coefficient decreases (or all others same, higher variance, the higher coefficient).
Which of the following is an example of an Interval measurement scale?
The temperature
Which of the following is a correct interpretation of the 60th percentile?
The value at which 60% of the distribution is below.
The researcher also finds there is strong, positive correlation between their reading comprehension scores and their shoe sizes for all children between grade 1 and 5, but there is almost no correlation between their reading comprehension and shoe sizes for all third graders. How did you explain these findings? Does it mean shoe sizes cause the good scores in reading comprehension, why or why not?
Their age. The older they are the bigger shoe size they wear which means they are also able to comprehend readings better than those who are younger.
It is suggested that males and females have different daily caloric intakes, with males able to consume a somewhat larger number of calories per day to maintain current weight levels. In the above tables, the averages for daily caloric intake for a sample of adult males and a sample of adult females are compared using a two-sample t-test. Examine the results in the above tables 1. what is the null Hypothesis for this study?
There is no difference between the caloric intake of females and males.
Data have been collected on how often adults feel they "eat healthy" during an average week. Responses include: "all the time," "most of the time," "sometimes," and "never." Which of the following graphs would be appropriate to use to graph this variable? Select all that apply. a. Bar graph b. Boxplot c. Histogram
a. Bar graph c. Histogram The histogram can demonstrate ordinal data such as the satisfaction of customers.
Which of the following is the preferred method of graphing data on the gender of a sample? a. Bar graph b. Frequency polygon c. histogram
a. Bar graph Explain your answers: Because in nominal values the order or rank is irrelevant. The bars in the graph are not linked or related they just show the frequency
1. What is the percentile rank of 80 in the normal distribution with mean=80 and SD(standard deviation)= 60 a) 10 b) 50 c) 80 d) 100
b) 50 Since the mean, mode and the median are the same the z score would be 0 and in the middle making it 50.
._________Which of the following properties is appropriate for ordinal, but not for nominal variables? a) A differs from B. b) A is greater than B. c) A is 10 units greater than B. d) A is twice as good as B.
b) A is greater than B.
For interval-level variables, which of the following properties does not apply? a) A is two units greater than B. b) A is greater than B. c) A is twice as good as B. d) A differs from B
c) A is twice as good as B.
Which of the following statements is correct for a continuous variable? a. The proportion of the distribution below the 25th percentile is 75%. b. The proportion of the distribution below the 50th percentile is 25%. c. The proportion of the distribution above the third quartile is 25%. d. The proportion of the distribution between the 25th and 75th percentile is 25%
c. The proportion of the distribution above the third quartile is 25%. Explain: continues variable can take any value in a range which is between 25th and 75th
the city wants to know the preference of dogs on the city's beaches. they construct a list of all the blocks of the city and randomly select 20% of the blocks to sample. they then survey all residents of the selected city blocks. This sampling is
cluster sampling
the researcher obtains a list of all elementary school districts in the states, randomly selects 5% of the districts, and administers achievement tests to all sixth graders in these districts, this sampling is
cluster sampling
A researcher observed that preschool children playing in a red room showed more aggression than children playing in a blue room. For this study, what is the independent variable?
color of the room
A researcher observed that preschool children playing a red room showed more aggression than children playing in a blue room. For this study, what is the independent variable?
color of the rooms
In order to know how Widener students' attitudes to final exams, Kate stands outside of a classroom and surveys existing students who took the finals, which sampling method did Kate use?
convenience sample
The null hypothesis is rejected when:
p <alpha (the level of significance)
An elementary school principal correlated the reading comprehension scores and the mathematics concept scores from a test, which correlation was probably the lowest?
for fourth graders with vocabulary scores above the school median
What is the correct statement of Null Hypothesis
it is the conjectures about the population that there is no effect.
A report issued by a research think tank states that the average teenager spends 9 hours per day on social media. Which measure is reflected in this statement?
mean
Mark is conducting research on the effects of the concussion protocol in professional football. Mark's population consists of all active professional football players in the National Football League (NFL). He wants to make sure that football players in both the the NFL's conferences (AFC and NFC) are proportionally represented. Which of the following sampling methods would be most appropriate?
stratified sampling
For a population with mean 80 and standard deviation 10, what is the Z-score that corresponds to a score of 60?
z=-2 Use the formula: Z score= (Raw score-Mean)/ SD (SD: standard deviation) = (60-80)/10=-2 in this case
Use the coefficient from the tables: Ŷ = 1.2X + 31, answer the following questions:1) What do Ŷ and X in the equation represent? (Hints: which one is the variable for level of experiences?
Ŷ represents the predicted income X represents the level of experience (10)
What would be the income of a newly hired employee in 20 years? Is this actual income or predicted income?
Ŷ= 1.2 (20) + 31 = 55 is the predicted income of an employee with 20 years' experience.It is a predicted income.
Suppose a researcher knows that the average number of beers consumed over spring break for Widener students is μ = 18 beers with a standard deviation of σ = 5. To determine whether or not a knowledge-based intervention program has an effect on student beer consumption, a researcher randomly selects 25 students from the population of Widener and asks them to participate in a week-long intervention before spring break. After Spring Break, the research found the average number of beers consumed over the spring break is 16. Did the knowledge-based intervention program have a significant effect on student beer consumption? Test with alpha set at .05. 1. Step One: State the Hypothesis What is the null hypothesis for this study H0:
μ = 18
What is the alternative hypothesis for this study Ha:
μ is not = 18
