# MS 150 Statistics t3 • Name:

ѵ (kph)
8.2
8.5
8.7
8.7
8.7
8.8
8.8
8.9
9.0
9.1
9.1
9.2
9.3
9.3
9.4
9.7

Last December I noted that my running had collapsed during the later half of 2009. I vowed to get back to the basics of my running. Running roughly an hour a day as often as possible if not daily. That was my goal. During the Christmas break, on 21 December, I launched into a regime of daily running. By the end of the first week of running I had attained 500 cumulutive minutes of running for seven days. On 19 March a critical statistic that I track, my three month average for the number of minutes of running per week, hit 400 minutes. That meant I had been running an average of 400 minutes per week for the past 90 days. The running I have done over the past three months is sometimes called LSD for "long slow distance" running. The data is my speed in kilometers per hour for the sixteen most runs that were ten kilometers in distance or longer. Note: the variable x is replaced by ѵ in the variables below.

Last December I noted that my running had collapsed during the later half of 2009. I vowed to get back to the basics of my running. Running roughly an hour a day as often as possible if not daily. That was my goal. During the Christmas break, on 21 December, I launched into a regime of daily running. By the end of the first week of running I had attained 500 cumulutive minutes of running for seven days. On 19 March a critical statistic that I track, my three month average for the number of minutes of running per week, hit 400 minutes. That meant I had been running an average of 400 minutes per week for the past 90 days. The running I have done over the past three months is sometimes called LSD for "long slow distance" running. The data is my speed in kilometers per hour for the sixteen most runs that were ten kilometers in distance or longer. Note: the variable x is replaced by ѵ in the variables below.

## Basic statistics

1. __________ Calculate the sample size n for the data.
2. __________ Calculate the sample mean ѵ.
3. __________ Calculate the sample standard deviation .

## Normal distribution

I often head out the door with a global positioning satellite receiver in hand. My speed for the first kilometer is usually a good gauge of my condition that particular day. Speeds below 8.5 kph are a sign that I have not sufficiently recovered from my run on the previous day. Speeds above 10 kph are usually a sign that I am going out too fast and need to back off the pace. That said, with the runs being normally distributed, there will be a percentage of them above or below these speeds.

1. p(ѵ ≤ 8.5) = _________ What percentage of my runs will be below 8.5 kph?
2. p(ѵ ≥ 10.0) = _________ What percentage of my runs will be above 10.0 kph?
3. p(ѵ ≤ _________) = 0.20 Below what speed would be the slowest 20% of my runs?

## Confidence interval

The data is for the most recent sixteen runs of ten kilometers or longer. The following questions ask you to calculate the 95% confidence interval for the population mean running speed - the average speed for all of my runs of ten kilometers or longer.

1. ____________________ Calculate the standard error SE of the mean.
2. ____________________ Calculate t-critical tc for a confidence level of 95%.
3. ____________________ Calculate the margin of error E for the mean.
4. p(__________ ≤ μ ≤ __________) = 0.95 Calculate the 95% confidence interval for the population mean μ running speed.

I run long distances slowly. This data looks at whether three months of long slow distance running had an impact on my speed. I was not training to run fast. My training focused on endurance. Running far. Every day. Not fast. Despite my focus on distance, did my speed also increase? A year ago in March 2009 my average speed for runs of 10 kilometers or longer was 8.73 kilometers per hour. Use the confidence interval data calculated above to determine the answer to the following questions.

1. ____________________ Does the 95% confidence interval include 8.73 kph?
2. ____________________ Based on the above, am I statistically significantly faster or slower than a year ago?