Question

(c) calculate an interval that includes at least 99% of the cadences in the population distribution using a confidence level of 95%. (round your answers to four decimal places.)

Answer 1

slader shows you how to do it

Answer 2

a. We are 95% confident that the true mean cadence for the population of healthy men is between 0.8856 and 0.9634 strides per second.

b. We are 95% confident that the cadence for a single randomly selected individual from this population is between 0.8898 and 0.9676 strides per second.

c. The interval includes at least 99% of the cadences in the population distribution with a confidence level of 95%.

How did we get these values?

(a) Calculate and interpret a 95% confidence interval for the population mean cadence.

`\[ \text{Confidence Interval} = 0.9245 \pm 2.093 \left((0.0831)/(√(20))\right) \]`

Calculations:

`\[ \text{Confidence Interval} = 0.9245 \pm 2.093 \left((0.0831)/(√(20))\right) \]`

Confidence Interval is approximately (0.9245 - 0.0389, 0.9245 + 0.0389)

Confidence Interval approximately (0.8856, 0.9634)

Interpretation: We are 95% confident that the true mean cadence for the population of healthy men is between 0.8856 and 0.9634 strides per second.

(b) Calculate and interpret a 95% prediction interval for the cadence of a single individual.

`\[ \text{Prediction Interval} = 0.9245 \pm 2.093 \left((0.0831)/(√(20))\right) * \sqrt{1 + (1)/(20)} * 0.0831 \]`

Calculations:

`\[ \text{Prediction Interval} = 0.9245 \pm 2.093 \left((0.0831)/(√(20))\right) * \sqrt{1 + (1)/(20)} * 0.0831 \]`

`\[ \text{Prediction Interval} \approx (0.8898, 0.9676) \]`

Interpretation: We are 95% confident that the cadence for a single randomly selected individual from this population is between 0.8898 and 0.9676 strides per second.

(c) Calculate an interval that includes at least 99% of the cadences in the population distribution using a confidence level of 95%.

`\[ \text{Interval} = 0.9245 \pm 2 * 0.0831 \]`

Calculations:

`\[ \text{Interval} = 0.9245 \pm 2 * 0.0831 \]`

`\[ \text{Interval} \approx (0.7583, 1.0907) \]`

This interval includes at least 99% of the cadences in the population distribution with a confidence level of 95%.

Complete question:

A study of the ability of individuals to walk in a straight line reported the accompanying data on cadence (strides per second) for a sample of n = 20 randomly selected healthy men. 0.91 0.85 0.92 0.95 0.93 0.87 1.00 0.92 0.85 0.81 0.77 0.93 0.93 1.03 0.93 1.06 1.09 0.96 0.81 0.97 A normal probability plot gives substantial support to the assumption that the population distribution of cadence is approximately normal. A descriptive summary of the data from Minitab follows. Variable N Mean Median TrMean StDev SEMean cadence 20 0.9245 0.9300 0.9239 0.0831 0.0186 Variable Min Max Q1 Q3 cadence 0.7700 1.0900 0.8600 0.9650

(a) Calculate and interpret a 95% confidence interval for population mean cadence. (Round your answers to four decimal places.) ,

(b) Calculate and interpret a 95% prediction interval for the cadence of a single individual randomly selected from this population. (Round your answers to four decimal places.) ,

(c) Calculate an interval that includes at least 99% of the cadences in the population distribution using a confidence level of 95%. (Round your answers to four decimal places.)