For test three you calculated some basic statistics for six laps run by my son Marlin. Subsequently I went up to the track to run six laps, and six laps only, as hard as I could to see what I could still do over a 2400 meter distance. Marlin's lap times and my lap times are reported in seconds in the table. Lower (smaller) lap times are faster lap times.
Marlin lap times (s)
Dana lap times (s)
168
136
162
134
158
129
164
138
153
126
143
122
_______________ Calculate the sample mean x for Marlin's lap time.
_______________ Calculate the sample mean x for Dana's lap time.
_____________ Are the sample means mathematically different?
_____________ What is the p-value? Perform an independent samples t-test using the TTEST function with two tails to determine the p-value for this two independent sample data. Do not run a paired t-test, the data is not paired data. Keep SIX decimal places.
_____________ Are the sample means statistically significantly different at a risk of a type I error alpha α = 0.05?
_____________________ Would we fail to reject| or |reject a null hypothesis of no difference in the sample means at a risk of a type I error alpha α = 0.05?
_____________ Calculate 1 ‒ (p‑value) to estimate the maximum level of confidence we can have that the difference in the means is statistically significant.
__________ Is Dana statistically significantly faster than Marlin at an alpha of 0.05?