Statistics Sample Questions with Solutions

Examine the variable GIFT in Appendix E of the Textbook

Directions: Answer all questions. Show all work as necessary for your explanation. If symbols are needed in representation of your solution, either describe the symbol…(e.g., x bar, for sample mean) or construct appropriate symbol using the equation editor in WORD. (This is NOT a requirement). Finally round all final answers to the nearest TWO decimals. Submit ANSWER Sheet NOT questions. (50pts)

1. Use the STUDENT INTEREST SURVEY and DATA found in Appendix E of the Textbook (pages A113-A115). Examine the Variable GIFT. For this variable: (NOTE: For the variable GIFT.

a) determine and label the 5-number summary. (2pts)
b) construct a box-and-whisker plot, label and identify the 5-number summary. (2pts)
c) identify the shape of the data set. (1pts)
d) calculate the interquartile range(IQR). (1pts)
e) if an outlier(s) exist(s), identify their value(s).(2pts)
f) Determine Percentile Rank of $200. Interpret its meaning in terms of the context of this problem. (2pts) 

2. A sample of the number of minutes spent on TikTok per day of college students is collected. A SUMMARY of the SAMPLE RESULTS are given in the following table:
Minutes Spent on TikTok per day
16 40 52 88 112 136
Z Score -1.5 -0.5 0 1.5 2.5 3.5
Percentile Rank 5 25 35 50 75 95
By inspection of the table, determine (The numbers in the table DO NOT REPRESENT ALL THE SAMPLE DATA VALUES):
a) The mean time spent on TikTok for ALL students in the sample. (2pts)
b) The median time spent on TikTok for ALL students in the sample. (2pts)
c) The percent of college students in the sample that spend between 52 and 136 minutes per day on TikTok. (2pts)
d) The number of minutes per day representing the 1ST quatile. (2pts)
e) The sample standard deviation. (2pts)
f) The interquartile range. (2pts)
g) The number of minutes per day for a z score of 4. (2pts)
h) The number of minutes per day that is 2.1 standard deviations below the mean. (2pts) 
3. The following data represents data collected by a social researcher to examine the relationship between “General Anxiety” and “Time Spent per day (Min/day) on TikTok. Each student completed both a personality inventory scale that yields a General Anxiety Scale Value and a survey indicating the number of Min/day the student spent on TikTok. The results are listed in the table below:
GENERAL
ANXIETY
39 55 62 95 40 48 5 27 83 82 42 47 45 79 15 8 81 75 20 10
TIME 75 45 42 84 25 41 15 31 109 70 43 55 61 56 44 21 99 84 26 15
Using the data:
a. Plot a scatter diagram of GENERAL ANXIETY value (Y AXIS) against Time (X AXIS). (4pts)
b. Compute a Pearson correlation coefficient for part a. (2pts)
c. Would you consider the correlation coefficient weak, moderately weak, moderately strong or strong? Why?(2pts)
d. Based on the data, do you believe GENERAL AXIETY is related to time spent on the social network site TikTok? Explain using your answer to part c (2pt)
e. Calculate the coefficient of determination for the correlation coefficient computed in part b.Explain the meaning of the coefficient of determination in the context of the variables. Be sure to identify the independent variable and dependent variable(4pts)
f. Determine the LINEAR regression Equation for the variables in this problem. Be sure to be consistent in your use of the independent and dependent variables (4pts)
g. Using the regression formula from part f predict a GENERAL ANXIETY SCORE based on the amount of time spent on the TikTok site for 100min/day. (4pts)
h. Is the prediction value in part g an example of Interpolation or Extrapolation? Explain. (2pts)