MS 150 Statistics t3 • Name:

The data is based on data from a physical science experiment that investigated the speed of sound. ^{1, 2}

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 classes (bins, intervals), what is the width of a single class?
12. Determine the frequency and calculate the relative frequency using five classes. Record your results in the table provided.

13. Sketch a frequency histogram of the data, labeling your horizontal axis and vertical axis as appropriate.
14. ____________________ What is the shape of the histogram?
15. __________ Theory predicts a speed of sound of 350 ms⁻¹. Calculate the z-score for a sound speed of 350 ms⁻¹ using the mean and standard deviation calculated above.
16. ____________________ Is a z-score for 350 ms⁻¹ ordinary or unusual?
17. ____________________ What is the point estimate for the population mean μ speed of sound?
18. ____________________ Calculate the standard error SE of the mean.
19. ____________________ Calculate the degrees of freedom n − 1.
20. ____________________ Calculate t-critical t_c for confidence levels of 95%.
21. ____________________ Calculate the margin of error E for the mean.
22. Calculate the 95% confidence interval for the population mean μ speed of sound.
    
    p(__________ ≤ μ ≤ __________) = 0.95
23. ____________________ Does the 95% confidence interval include 350 ms⁻¹?
24. ____________________ Sound speed theory states that the speed of sound is 350 ms⁻¹. Is 350 ms⁻¹ a possible population mean μ for this sample at a confidence level of 95%?
25. ____________________ Based on the data provided, would we disconfirm or fail to disconfirm a theory that stated the speed of sound is 350 ms⁻¹?

Confidence interval statistics
Statistic or Parameter	Symbol	Equations	OpenOffice
Degrees of freedom	df	n − 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