Question

**Foot-Length:** It has been claimed that, on
average, right-handed people have a left foot that is larger than
the right foot. Here we test this claim on a sample of 10
right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.01
significance level. You may assume the sample of differences comes
from a normally distributed population.

Person | Left
Foot (x) |
Right
Foot (y) |
difference (d = x − y) |

1 | 272 | 272 | 0 |

2 | 268 | 267 | 1 |

3 | 259 | 261 | -2 |

4 | 255 | 254 | 1 |

5 | 261 | 258 | 3 |

6 | 273 | 273 | 0 |

7 | 272 | 270 | 2 |

8 | 258 | 256 | 2 |

9 | 273 | 272 | 1 |

10 | 255 | 253 | 2 |

Mean | 264.60 | 263.60 | 1.00 |

s |
7.71 | 8.04 | 1.41 |

If you are using software, you should be able copy and paste the
data directly into your software program.

(a) The claim is that the mean difference is positive
(*μ*_{d} > 0). What type of test is
this?

This is a two-tailed test.

This is a right-tailed test.

This is a left-tailed test.

(b) What is the test statistic? **Round your answer to 2
decimal places.**

*t*

_{d}

=

*To account for hand calculations -vs- software, your answer
must be within 0.01 of the true answer.*

(c) Use software to get the P-value of the test statistic.
**Round to 4 decimal places.**

P-value =

(d) What is the conclusion regarding the null hypothesis?

reject *H*_{0}

fail to reject
*H*_{0}

(e) Choose the appropriate concluding statement.

The data supports the claim that, on average, right-handed people have a left foot that is larger than the right foot.

There is not enough data to support the claim that, on average, right-handed people have a left foot that is larger than the right foot.

We reject the claim that, on average, right-handed people have a left foot that is larger than the right foot.

We have proven that, on average, right-handed people have a left foot that is larger than the right foot.

Answer #1

a)

right tailed test

b)

c)

from the above software result p value =
**0.0261**

d)

fail to reject H0

we are allowed to solve four sub parts only.

Foot-Length: It has been claimed that, on
average, right-handed people have a left foot that is larger than
the right foot. Here we test this claim on a sample of 10
right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.05
significance level. You may assume the sample of differences comes
from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
difference (d = x − y)...

Foot-Length: It has been claimed that, on
average, right-handed people have a left foot that is larger than
the right foot. Here we test this claim on a sample of 10
right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.05
significance level. You may assume the sample of differences comes
from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
difference (d = x − y)...

Foot-Length: It has been claimed that, on
average, right-handed people have a left foot that is larger than
the right foot. Here we test this claim on a sample of 10
right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.05
significance level. You may assume the sample of differences comes
from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
difference (d = x − y)...

Foot-Length (Raw Data, Software
Required):
It has been claimed that, on average, right-handed people have a
left foot that is larger than the right foot. Here we test this
claim on a sample of 10 right-handed adults. The table below gives
the left and right foot measurements in millimeters (mm). Test the
claim at the 0.01 significance level. You may assume the sample of
differences comes from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
1
274...

Foot-Length: It has been claimed that, on
average, right-handed people have a left foot that is larger than
the right foot. Here we test this claim on a sample of 10
right-handed adults. The table below gives the left and right foot
measurements in millimeters (mm). Test the claim at the 0.01
significance level. You may assume the sample of differences comes
from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
difference (d = x − y)...

Foot-Length (Raw Data, Software
Required):
It has been claimed that, on average, right-handed people have a
left foot that is larger than the right foot. Here we test this
claim on a sample of 10 right-handed adults. The table below gives
the left and right foot measurements in millimeters (mm). Test the
claim at the 0.01 significance level. You may assume the sample of
differences comes from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
1
273...

Foot-Length (Raw Data, Software
Required):
It has been claimed that, on average, right-handed people have a
left foot that is larger than the right foot. Here we test this
claim on a sample of 10 right-handed adults. The table below gives
the left and right foot measurements in millimeters (mm). Test the
claim at the 0.01 significance level. You may assume the sample of
differences comes from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
1
270...

Foot-Length (Raw Data, Software
Required):
It has been claimed that, on average, right-handed people have a
left foot that is larger than the right foot. Here we test this
claim on a sample of 10 right-handed adults. The table below gives
the left and right foot measurements in millimeters (mm). Test the
claim at the 0.05 significance level. You may assume the sample of
differences comes from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
1
268...

The vast majority of people have hand dominance--they are either
left-handed or right-handed.
In this question we will ignore the very small percentage of the
population who are
ambidextrous (i.e., those who use both hands equally well or
equally badly!).
A researcher believes that men are more likely to be left-handed
than women. To check this she
checked the dominant hand of random samples of 200 men and 200
women, and found 24 men
and 18 women to be left-handed....

6. It is widely accepted that people are a little taller in the
morning than at night. Here we perform a test on how big the
difference is. In a sample of 34 adults, the mean difference
between morning height and evening height was 5.6 millimeters (mm)
with a standard deviation of 1.8 mm. Test the claim that, on
average, people are more than 5 mm taller in the morning than at
night. Test this claim at the 0.10 significance...

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