Question

**Sibling IQ Scores (Raw Data, Software
Required):**

There have been numerous studies involving the correlation and
differences in IQ's among siblings. Here we consider a small
example of such a study. We will test the claim that, on average,
older siblings have a higher IQ than their younger sibling. The
results are depicted for a sample of 10 siblings in the table
below. Test the claim at the 0.05 significance level. You may
assume the sample of differences comes from a normally distributed
population.

Pair ID | Older
Sibling IQ (x) |
Younger Sibling IQ(y) |

1 | 83 | 79 |

2 | 86 | 89 |

3 | 90 | 86 |

4 | 91 | 91 |

5 | 98 | 94 |

6 | 103 | 101 |

7 | 104 | 104 |

8 | 109 | 108 |

9 | 113 | 107 |

10 | 120 | 112 |

You should be able copy and paste the data directly into your
software program.

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

This is a two-tailed test.

This is a left-tailed test.

This is a right-tailed test.

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

*t*_{d}=

(c) What is 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, older siblings have a higher IQ than their younger sibling.

There is not enough data to support the claim that, on average, older siblings have a higher IQ than their younger sibling.

We reject the claim that, on average, older siblings have a higher IQ than their younger sibling.

We have proven that, on average, older siblings have a higher IQ than their younger sibling.

Answer #1

The statistical software output for this problem is:

Hence,

a) This is a **right tailed** test.

b) Test statistic = **2.54**

c) P - value = **0.0159**

d) **Reject Ho**

e) **The data supports the claim that, on average, older
siblings have a higher IQ than their younger sibling.**

Sibling IQ Scores (Raw Data, Software
Required):
There have been numerous studies involving the
correlation and differences in IQ's among siblings. Here we
consider a small example of such a study. We will test the claim
that, on average, older siblings have a higher IQ than their
younger sibling. The results are depicted for a sample of 10
siblings in the table below. Test the claim at the 0.05
significance level. You may assume the sample of differences comes
from...

Sibling IQ Scores (Raw Data, Software Required): There have been
numerous studies involving the correlation and differences in IQ's
among siblings. Here we consider a small example of such a study.
We will test the claim that, on average, older siblings have a
higher IQ than their younger sibling. The results are depicted for
a sample of 10 siblings in the table below. Test the claim at the
0.05 significance level. You may assume the sample of differences
comes from...

Sibling IQ Scores (Raw Data, Software
Required):
There have been numerous studies involving the correlation and
differences in IQ's among siblings. Here we consider a small
example of such a study. We will test the claim that, on average,
older siblings have a higher IQ than their younger sibling. The
results are depicted for a sample of 10 siblings in the table
below. Test the claim at the 0.01 significance level. You may
assume the sample of differences comes from...

Sibling IQ Scores: There have been numerous
studies involving the correlation and differences in IQ's among
siblings. Here we consider a small example of such a study. We will
test the claim that, on average, older siblings have a higher IQ
than their younger sibling. The results are depicted for a sample
of 10 siblings in the table below. Test the claim at the 0.05
significance level. You may assume the sample of differences comes
from a normally distributed population....

Sibling IQ Scores: There have been numerous
studies involving the correlation and differences in IQ's among
siblings. Here we consider a small example of such a study. We will
test the claim that, on average, older siblings have a higher IQ
than their younger sibling. The results are depicted for a sample
of 10 siblings in the table below. Test the claim at the 0.01
significance level. You may assume the sample of differences comes
from a normally distributed population....

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...

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 (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 0.01 significance level. You may assume the sample of
differences comes from a normally distributed population.
Person
Left
Foot (x)
Right
Foot (y)
1
273...

Math & Music (Raw Data, Software
Required):
There is a lot of interest in the relationship between studying
music and studying math. We will look at some sample data that
investigates this relationship. Below are the Math SAT scores from
8 students who studied music through high school and 11 students
who did not. Test the claim that students who study music in high
school have a higher average Math SAT score than those who do not.
Test this claim...

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