Quan 571
Midterm
Spring 2022 Ins.: G. Nazi
Name:
⦁ The manager of Jerry’s Barbershop recently asked 25 customers to punch in a timecard when first arrive at the shop and to punch out right after they paid for their haircut and used the data on the cards to measure how long (in minutes) it took Jerry and his barbers to cut hair. The summary of the times it took Jerry and his barbers to cut hair is summarized below. Jerry also recorded the amount of money spent by each of the 25 customers as well as the customer’s stage of life (Child, Teen, or Adult).
Summary of the times in minutes.
⦁ Identify the population in this study. (2 pts.)
Population:
⦁ Identify the variables and units: (5 pts.)
Variable-1: units:
Variable-2: units:
Variable-2: units:
⦁ Is the study univariate, bivariate or multivariate? Explain. (2 pts.)
Type of study:
Explain:
⦁ What is the sample size? Is it large or small? Explain. (3 pts.)
Sample size:
Large or small:
Explain:
⦁ Describe the distribution of the times it takes Jerry and his barbers to cut hair (i.e. symmetrical, right skewed, … etc.). Justify your answer. (2 pts.)
Type of distribution:
Justify:
⦁ What percent of Jerry’s customers cut their hair in less than 20 minutes? Justify your answer. (2 pts.)
Percent =
Justify:
⦁ Show that H = 32 minutes is an outlier. Show all the work. (7 pts.)
IQR =
LB =
UB =
Explain:
⦁ Is the mean (22 minutes) or median (16 minutes) the better measurement of the center for the times? Explain. (2 pts.)
Best measurement of center:
Explain:
⦁ What is the best measurement for spread for the times. (1 pt.)
Best measurement of spread:
⦁ Blood is grouped into four types: A, B, AB, and O. The percent of Americans with each type are as follows: O, 43%; A, 40%; B, 12%; and AB, 5%. At a recent blood drive at a large university, the donors were classified as shown below. s there sufficient evidence to conclude that the proportions differ from those stated above?
⦁ Find the expected frequencies. Fill in the table below. (6 pts.)
Blood Type O E
A 60
B 65
AB 15
O 10
⦁ Write the Null and the Alternative hypotheses. (2 pts.)
:
⦁ Find the p-value = (2 pts.)
⦁ Write the decision, Reject or Fail to Reject (1 pt.)
Decision:
⦁ Write the conclusion in context of this problem. (2 pts.)
Conclusion:
⦁ Is age independent of the desire to ride a bicycle? A random sample of people was surveyed. Each person was asked their interest in riding a bicycle (Variable A) and their age (Variable B). The data that resulted from the survey is summarized in the following table:
Is there evidence to conclude that the desire to ride a bicycle depends on age?
⦁ Find the expected frequencies. Round off to one decimal. Fill in the table below. (8 pts.)
⦁ Write the Null and the Alternative hypotheses. (2 pts.)
:
⦁ Find the p-value = (2 pts.)
⦁ Write the decision, Reject or Fail to Reject (1 pt.)
Decision:
⦁ Write the conclusion in context of this problem. (2 pts.)
Conclusion:
⦁ A district wishes to study the relationship between class size (x), and achievement test scores (y). A sample of 15 classrooms from the school district is shown in the scatterplot below.
⦁ Does the scatter plot suggest a linear correlation between class size (x), and achievement test scores (y)? If yes, what type of linear correlation exists? Why? (3 pts.)
Yes or No:
If yes, what type:
Explain:
⦁ Interpret in context of this problem. (2 pts.)
Answer:
⦁ Use the regression equation to predict the achievement score for a class of size 22. (1 pt.)
Answer:
⦁ Test the claim “There is a significant linear correlation between class size (x), and achievement test scores (y)
⦁ Write the Null and the Alternative hypotheses. (2 pts.)
:
⦁ Find the degrees of freedom. (1 pt.)
df =
⦁ Find the t = (3 pts.)
⦁ Find the p-value = (3 pts.)
⦁ Write the decision, Reject or Fail to Reject (1 pt.)
Decision:
⦁ Write the conclusion in context of this problem. (2 pts.)
Conclusion:
⦁ Is the linear model a valid model? Comment using the residual plot below. (3 pts.)
Yes or No:
Explain:
⦁ Multiple choice (1 pt. each)
Type the letter that corresponds to the answer in the answer box provided at the end of this question.
⦁ The science of Descriptive statistics includes which of the following:
⦁ Organizing data.
⦁ Presenting data.
⦁ Summarizing data.
⦁ All of the above.
⦁ In Inferential statistics our main objective is to:
⦁ Describe the population.
⦁ Describe the data we collected.
⦁ Infer something about the population.
⦁ Compute an average.
⦁ Which of the following statements is true regarding a sample?
⦁ It is a part of population.
⦁ It must contain at least five observations.
⦁ It must be normally distributed.
⦁ All of the above.
⦁ A quantitative variable:
⦁ Always refers to a sample.
⦁ Is not numeric.
⦁ Have only two possible outcomes.
⦁ None of the above.
⦁ A continuous variable is:
⦁ An example of a qualitative variable.
⦁ Must be ordinal.
⦁ Must appear in the form of a count.
⦁ Must appear in the form of a measurement.
⦁ A study is conducted to find out the percent of High School seniors attend a four-year college. The population is:
⦁ All four-year colleges.
⦁ All High School seniors.
⦁ The percent of High School seniors.
⦁ All High School seniors attending a four-year college.
⦁ Age is an example of
⦁ Discrete data.
⦁ Continuous data.
⦁ Qualitative data.
⦁ None of the above.
⦁ Blood types is an example of
⦁ Nominal data
⦁ Ordinal data
⦁ Interval data
⦁ Ratio data
Use the scenario below for question 9
The ages of patients admitted to the emergency room over a weekend is normally distributed with a mean of 52 years and standard deviation of 8 years. Forty patients were used for this study.
⦁ What is the variable in this study?
⦁ Age (in years).
⦁ The forty patients used for this study
⦁ All patients admitted to the emergency room.
⦁ All patients admitted to the emergency room over a weekend
⦁ Zip codes are:
:
⦁ Qualitative data
⦁ Continuous data
⦁ Discrete data
⦁ Quantitative data
⦁ None of the above
⦁ A random sample of 500 households in Vancouver was selected and several variables are recorded for each household. Which of the following is NOT CORRECT? :
a) Household total income is a ratio scaled variable.
b) Household total income is a quantitative variable.
c) Socioeconomic status was coded as low income, middle income, and high income is an interval scaled variable.
d) The primary language used at home is a nominal scaled variable.
⦁ A chi-square test is used to test whether a 0 to 9 spinner is “fair” (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The expected counts for spinning a 5 will be
⦁ 5 b. 10 c. 11 d. 20
⦁ Phone numbers gathered from all Felician College students.
⦁ Qualitative
⦁ Quantitative
⦁ High temperatures in Celsius are recorded daily at the local weather station.
⦁ Nominal
⦁ Ordinal
⦁ Interval
⦁ Ratio
⦁ Social security numbers
⦁ Qualitative
⦁ Quantitative
⦁ The names of various tree species are gathered and recorded.
⦁ Nominal
⦁ Ordinal
⦁ Interval
⦁ Ratio
⦁ The number of trees in each acre of forest is monitored by the forestry service.
⦁ Nominal
⦁ Ordinal
⦁ Interval
⦁ Ratio
⦁ The states of health for randomly selected tree trees are classified as “poor”, “good”, or “very good”.
⦁ Nominal
⦁ Ordinal
⦁ Interval
⦁ Ratio
⦁ The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year. She wants to know if each type of food will be equally popular so she can start ordering supplies. To find out, she selects a random sample of 100 students and asks them, “Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?” Here are the data in the table provided. An appropriate null hypothesis would be….
Type of Food Asian Mexican Pizza Hamburgers
Count 22 28 20 30
⦁ The observed distribution of food preference is different than last year.
⦁ The observed distribution of food preference is the same as last year.
⦁ The observed distribution of food preference is different than the expected uniform distribution.
⦁ The observed distribution of food preference is the same as the expected uniform distribution.
⦁ Describe the shape of the distribution?
⦁ Uniform
⦁ Right skewed
⦁ Left skewed.
⦁ Bell shaped.
⦁ If the correlation between body weight (y) and annual income (x) were high and positive, we could conclude that:
a) High incomes cause people to eat less food.
b) Low incomes cause people to eat more food.
c) High incomes cause people to eat more food.
d) High income people tend to be less heavy than low-income people, on average.
⦁ Men tend to marry women who are slightly younger than themselves. Suppose that every man (x) married a woman (y) who was exactly 0.5 of a year younger than themselves. Which of the following is CORRECT?
a) The correlation is −0.5.
b) The correlation is 0.5.
c) The correlation is 1.
d) The correlation is 0
⦁ Which is the strongest relationship?
⦁ r = -0.582
⦁ r = 0.582
⦁ r = -0.822
⦁ Not enough information
⦁ In a statistics course, a linear regression equation was computed to predict the final exam score based on the score on the first test of the term. The equation was, , where y is the final exam score and x is the score on the first test. George scored 80 on his first test, what is his predicted final exam score?
⦁ 80
⦁ 81
⦁ 82
⦁ 91
⦁ A study is conducted to test the claim that there is a positive correlation between Age and IQ scores among adult males. Use the information below to estimate the p-value for the study
n = 20
t = 2.791
a) 0.01 < p < 0.02
b) 0.005 < p < 0.01
c) 0.001 < p < 0.005
d) 0.002 < p < 0.01
Answers: Type the letter that corresponds to the answer.
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25