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.

0.95 | 0.85 | 0.92 | 0.95 | 0.93 | 0.87 | 1.00 | 0.92 | 0.85 | 0.81 |

0.78 | 0.93 | 0.93 | 1.03 | 0.93 | 1.06 | 1.07 | 0.96 | 0.81 | 0.95 |

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 | 0.9250 | 0.9300 | 0.9250 | 0.0798 | 0.0178 |

Variable | Min | Max | Q1 | Q3 | ||

cadence | 0.7800 | 1.0700 | 0.8600 | 0.9550 |

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

- With 95% confidence, the value of the true mean cadence of all
such men falls below the confidence interval.

- With 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval.

- With 95% confidence, the value of the true mean cadence of all
such men falls above the confidence interval. strides per
second

Interpret this interval.

(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.), strides per second

Interpret this interval.

- If this bound is calculated once, there is a 5% chance that these bounds will capture a future individual value of cadence for a healthy man.

- If this bound is calculated once, there is a 95% chance that these bounds will capture a future individual value of cadence for a healthy man.

- If this bound is calculated sample after sample, in the long run, 95% of these bounds will capture a future individual value of cadence for a healthy man.

- If this bound is calculated sample after sample, in the long run, 95% of these bounds will fail to capture a future individual value of cadence for a healthy man.

Answer #1

Here we have

(a)

Degree of freedom : df n -1=19

Critical value of t for 95% confidence interval is
**2.093.**

**So requried confidence interval is**

So requried confidence interval is (0.8877, 0.9623).

correct option is :

With 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval.

(b)

**So requried prediction interval is**

So requried confidence interval is (0.7539, 1.0961).

Correct option:

If this bound is calculated sample after sample, in the long run, 95% of these bounds will capture a future individual value of cadence for a healthy man.

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