# 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 =STDEV(data)/SQRT(sample size n)
Calculate a margin of error for the mean E for n ≥ 5 using sx. E =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