MS 150 quiz 12 § 11.1 • Name:

24 April 2009

When a road runner runs a route a common goal of runners is to run a negative split. A negative split means to run the second half of the route faster than the first half. I often run to Nett bridge and back, or down to Lidakida beach and back. On these "out-and-back" runs I usually push for a negative split. Sometimes I do not get a negative split, and the time differences are always small. Both routes are tough to negative split, the outbound is downhill and the inbound return is uphill. Do the seven runs below indicate that I am statistically significantly faster on the inbound return than on the outbound run?

Route	Outbound time (min)	Inbound time (min)	Diff
Nett Bridge	22.25	20.38	-1.87
Nett Bridge	22.97	21.12	-1.85
Lidakida	16.97	16.05	-0.92
Lidakida	20.32	19.43	-0.89
Nett Bridge	22.67	22.13	-0.54
Lidakida	16.12	15.87	-0.25
Nett Bridge	26.75	27.25	0.5
1.	Sample size n
2.	Sample mean x
3.	Standard deviation sx
4.	Standard error SE
5.	t-critical for alpha α = 0.05
6.	Margin of error E
7.	Lower bound ci
8.	Upper bound ci
9.	p-value from t-test for paired data
10.	maximum confidence level c

__________ Does the 95% confidence interval for the mean of the paired differences include zero?
__________ Am I statistically significantly faster (shorter time) on the inbound return than on the outbound run at an alpha of 5%?
__________ If I am indeed faster inbound, as a percentage how sure can you be that I am faster?
____________________ Should you reject or fail to reject the null hypothesis?
__________ If you reject the null hypothesis H₀: μ_diff= 0, what is the risk that you will wrong?

Hypothesis Testing
Statistic or Parameter	Symbol	Equations	OpenOffice
Relationship between confidence level c and alpha α for two-tailed tests		1 − c = α
Calculate t-critical for a two-tailed test using α = 0.05:	t_c		=TINV(α;df)
Calculate a t-statistic t	t		=(x - μ)/(sx/SQRT(n))
Calculate a two-tailed p-value from a t-statistic	p-value		= TDIST(ABS(t);df;2)