MS 150 Statistics t3 • Name:

Index of refraction
1.25
1.25
1.23
1.18
1.58
1.50
1.14
1.16
1.09
1.16
1.26
1.23

The data is from a physical science experiment that investigated the index of refraction of water obtained on .

  1. __________ Find the sample size n for the data.
  2. __________ Find the minimum.
  3. __________ Find the maximum.
  4. __________ Find the range.
  5. __________ Find the midrange.
  6. __________ Find the median.
  7. __________ Find the mode.
  8. __________ Find the sample mean x.
  9. __________ Find the sample standard deviation sx.
  10. __________ Find the sample coefficient of variation CV.
  11. __________ If this data is divided into five bins, what is the width of a single bin?
  12. Determine the frequency and calculate the relative frequency using five bins (classes, intervals). Record your results in the table provided.
Bin upper limitsFrequency FRelative Frequency
Sums:
  1. Sketch a frequency histogram of the data, labeling your horizontal axis and vertical axis as appropriate.
  2. ____________________ What is the shape of the histogram?
  3. __________ The index of refraction for water is 1.33. Calculate the z-score for an index of refraction of 1.33 using the mean and standard deviation calculated above.
  4. ____________________ Is a z-score of 1.33 ordinary or unusual?
  5. __________ The index of refraction for glass is 1.5. Calculate the z-score for an index of refraction of 1.5 using the mean and standard deviation calculated above.
  6. ____________________ Is a z-score of 1.5 ordinary or unusual?
  7. ____________________ What is the point estimate for the population mean μ?
  8. ____________________ Calculate the standard error of the mean SE.
  9. ____________________ Calculate the degrees of freedom n − 1.
  10. ____________________ Calculate t-critical tc for confidence levels of 95%.
  11. ____________________ Calculate the margin of error for the mean E.
  12. Calculate the 95% confidence interval for the population mean μ total rainfall.

    p(__________ ≤ μ ≤ __________) = 0.95
  13. ____________________ Does the 95% confidence interval include 1.33?
  14. ____________________ Refraction theory states that the index of refraction for water is 1.33. Is 1.33 a possible population mean μ for this sample at a confidence level of 95%?
  15. ____________________ Would we disconfirm or fail to disconfirm an index of refraction of 1.33 for water?
Confidence interval statistics
Statistic or ParameterSymbolEquationsOpenOffice
Degrees of freedomdfn − 1 =COUNT(data)-1
Find a tcritical value from a confidence level c tc =TINV(1-c;df)
Standard error of the sample mean SE SE sx =STDEV(data)/SQRT(sample size n)
Calculate a margin of error for the mean E for n ≥ 5 using sx. E error tolerance tc =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean μ from a sample mean x and an error tolerance E x − E ≤ μ ≤ x + E