sf1 103 echo

Grid 12 x 10 on the thirties background rectangle major grid lines axes data points as triangles text layers Plastic beads x-axis x-axis labels 0 40 80 120 160 200 240

  1. Consider the horizontal distribution of plastic beads on the floor as depicted in the diagram. What is the horizontal mean for this plastic bead distribution?
  2. What is the horizontal standard deviation for the plastic bead distribution?
  3. Does the horizontal bead distribution appear to be roughly a normal distribution?
Speed (kph)
8.7
8.6
9.9
8.7
9.9
6.9
8.1
9.6
6.9
9.0
3.2
9.9
7.7
8.7
6.9
8.7
6.9
9.9

As an aging runner my speed will naturally decrease with age. On Sunday 15 March I ran 18.5 km, keeping track of my speed in kilometers per hour for each kilometer of the run. The data in the table was recorded photographically and is available in a blog on that long run. Use this data for the rest of the test.

For non-terminating decimals, report answers to two decimal places.

  1. Calculate the sample size n: _
  2. Calculate the sample mean x: _
  3. Calculate the sample standard deviation sx: _

    Confidence interval

  4. Calculate the standard error SE of the sample mean x: _
  5. Calculate tcritical for a confidence level c of 95%: _
  6. Calculate the margin of error E for the sample mean x: _
  7. Calculate the lower bound for the 95% confidence interval for the mean: _
  8. Calculate the upper bound for the 95% confidence interval for the mean: _
  9. In 2009, five and half years ago, I ran a ten kilometer run at 8.54 kilometers per hour. If the confidence interval includes 8.54 kph, then I am neither faster nor slower than I was in 2009. Does the current data include 8.54 kph in the 95% confidence interval?
  10. Can you reject a speed of 8.54 kph based on this data, or does the data support a speed of 8.54 m/s?

    Hypothesis testing

    At a risk of a type I error alpha α = 0.05, run a hypothesis test using the same data with a null hypothesis of
    H0: μ = 8.54

    and an alternate hypothesis of
    H1: μ ≠ 8.54

  11. Calculate tcritical with the risk of a type I error at 5%:_
  12. Calculate the t-statistic t:_
  13. Use =TDIST(ABS(t),n−1,2) to calculate the p-value:_
  14. Is the sample mean x significantly different from the population mean μ of 8.54 at an alpha α of 0.05?
  15. At an alpha α of 5%, would you fail to reject |or| reject the null hypothesis?
  16. Based on the analysis above is my running speed significantly different from my speed in 2009 at an alpha α of 5%?
  17. Based on the above analysis, am I now running slower than I was in 2009?
  18. Based on the above analysis, am I now running faster than I was in 2009?