Statistics

MAT 107

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Directions: Please complete the following statistical analyses for the sample data that accompanies this project. If you do the work for this project by hand, you must show the work you do to arrive at your results. If you use technology (Excel, graphing calculator, etc.) to obtain the results, you must state the technology you used to obtain the results.

 

 

  1. (5 points) Construct a grouped frequency distribution for the sample data. Use 6 classes. Use the minimum data value as the lower limit of the first class.

 

Class

Limits

Class

Boundaries

Frequency Relative

Frequency

Cumulative Frequency
 

 

       
 

 

       
 

 

       
 

 

       
 

 

       
 

 

       

 

 

 

  1. (3 points) Draw a histogram for the data set. Title the graph and label the axes appropriately.

 

 

 

 

 

 

 

 

 

 

 

  1. (2 points) Does the distribution appear to be normal (yes or no)? Explain.
    4. (6 points) Find the following descriptive statistics for the sample data.

 

Mean

Median Mode(s)
     

 

Range Variance Standard Deviation
     

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. (3 points) Find the 5-number summary for the data.

 

Min = _______________

 

Q1  = _______________

 

Q2  = _______________

 

Q3  = _______________

 

Max = _______________

 

 

 

  1. (2 points) Sketch a box plot. Do your best to draw it to scale.

 

 

 

 

 

 

 

 

  1. (1 point) What is the IQR for this data set? ____________

 

 

 

 

  1. (3 points) Outlier identification

 

 

Any data value less than ________or greater than_______ is to be considered an outlier.

 

Therefore, the following data values are outliers (write “none” if there are no outliers):

 

  1. (3 points) Construct a 95% confidence interval for the population’s mean.

 

 

 

____________ < μ < ____________

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. (2 points) If someone were to ask you what this particular confidence interval means, what would you say?

 

 

 

 

 

11. (5 points) Test the hypothesis that the population’s mean is different from the sample’s median value.

Use α = 0.05.

 

 

Alternative hypothesis (H1): ________________

 

 

Null hypothesis (H0): _____________________

 

 

Critical value: ____________

 

 

Test statistic: ____________

 

 

Conclusion:

Do you reject the null hypothesis(yes or no)? _________

 

 

If someone were to ask what the conclusion means in this particular study, what would you say?

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