The resting heart rate in beats per minute for the ESS 101j Joggling students are shown in the table.
RHR/bpm |
---|
62 |
63 |
65 |
68 |
68 |
68 |
69 |
69 |
71 |
72 |
77 |
79 |
79 |
82 |
83 |
86 |
88 |
91 |
94 |
94 |
For the resting heart rate data:
Bins | Frequency | Relative Frequency f/n |
---|---|---|
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
Sums: | _________ | _________ |
Part two explores whether there is a relationship for the Joggling class students between their resting heart rates (RHR)in beats per minute and their body fat index (BFI).
RHR | BFI |
---|---|
62 | 10.8 |
63 | 14.5 |
65 | 16.4 |
68 | 05.5 |
68 | 11.7 |
68 | 30.5 |
69 | 11.3 |
69 | 21.7 |
71 | 23.7 |
72 | 33.5 |
77 | 23.5 |
79 | 20.6 |
79 | 31.2 |
82 | 17.8 |
83 | 45.5 |
86 | 34.9 |
88 | 38.1 |
91 | 21.8 |
94 | 34.0 |
94 | 45.9 |
Basic Statistics | |||
---|---|---|---|
Statistic or Parameter | Symbol | Equations | Excel |
Square root | =SQRT(number) | ||
Sample size | n | =COUNT(data) | |
Sample mean | x | Σx/n | =AVERAGE(data) |
Sample standard deviation | sx or s | =STDEV(data) | |
Sample Coefficient of Variation | CV | sx/x | =STDEV(data)/AVERAGE(data) |
Linear Regression Statistics | |||
---|---|---|---|
Statistic or Parameter | Symbol | Equations | Excel |
Slope | b | =SLOPE(y data, x data) | |
Intercept | a | =INTERCEPT(y data, x data) | |
Correlation | r | =CORREL(y data, x data) | |
Coefficient of Determination | r^{2} | =(CORREL(y data, x data))^2 |
Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|
Normal Statistics | |||
Calculate a z value from an x | z | ^{=} | =STANDARDIZE(x, µ, σ) |
Calculate an x value from a z | x | = σ z + µ | =σ*z+µ |
Calculate an x from a z | =µ + z_{c}*sx/sqrt(n) | ||
Find a probability p from a z value | =NORMSDIST(z) | ||
Find a z value from a probability p | =NORMSINV(p) | ||
Confidence interval statistics | |||
Degrees of freedom | df | = n-1 | =COUNT(data)-1 |
Find a z_{c} value from a confidence level c | z_{c} | =ABS(NORMSINV((1-c)/2)) | |
Find a t_{c} value from a confidence level c | t_{c} | =TINV(1-c,df) | |
Calculate an error tolerance E of a mean for n ≥ 30 using sx | E | =z_{c}*sx/SQRT(n) | |
Calculate an error tolerance E of a mean for n < 30 using sx. Should also be used for n ≥ 30. | E | =t_{c}*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 | ||
Hypothesis Testing | |||
Calculate t-critical for a two-tailed test | t_{c} | =TINV(α,df) | |
Calculate a t-statistic | t | =(x - µ)/(sx/SQRT(n)) | |
Calculate a two-tailed p-value from a t-statistic | p | = TDIST(ABS(t),df,2) |