Question

A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey?

Attitude | 1st Survey | 2nd Survey |
---|---|---|

Optimistic | 7% | 6% |

Slightly Optimistic | 9% | 6% |

Slightly Pessimistic | 31% | 37% |

Pessimistic | 53% | 51% |

Copy Data

Step 6 of 10 :

Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem

Step 8 of 10: Find the critical value of the test at the 0.025 level of significance. Round your answer to three decimal places

Answer #1

step 6:

Applying chi square test of independence: |

Expected |
E_{i}=row total*column
total/grand total |
1st survey | 2nd survey | Total |

Optimistic | 16.2500 | 16.2500 | 33 | |

Slightly optimistic | 18.7500 | 18.7500 | 38 | |

Slightly Pessimistic | 85.0000 | 85.0000 | 170 | |

Pessimistic | 130.0000 | 130.0000 | 260 | |

total | 250 | 250 | 500 | |

chi
square χ^{2} |
=(O_{i}-E_{i})^{2}/E_{i} |
1st survey | 2nd survey | Total |

Optimistic | 0.096 | 0.096 | 0.1923 | |

Slightly optimistic | 0.750 | 0.750 | 1.5000 | |

Slightly Pessimistic | 0.662 | 0.662 | 1.3235 | |

Pessimistic | 0.048 | 0.048 | 0.0962 | |

total | 1.5560 | 1.5560 | 3.1120 | |

test statistic
X^{2}= |
3.112 |

Step 7 of 10:

degree of freedom(df) =(rows-1)*(columns-1)= |
3 |

step 8 of 10:

for 3 df and 0.025 level,critical value χ2= |
9.348 |

A psychologist conducted a survey of the attitude towards the
sustainability of American energy consumption with 250 randomly
selected individuals several years ago. The psychologist believes
that these attitudes have changed over time. To test this he
randomly selects 250 individuals and asks them the same questions.
Can the psychologist confirm his theory that the attitudes have
changed from the first survey to the second survey?
Attitude 1st Survey 2nd Survey
Optimistic 7% 5%
Slightly Optimistic 11% 18%
Slightly Pessimistic...

A psychologist conducted a survey of the attitude towards the
sustainability of American energy consumption with 230 randomly
selected individuals several years ago. The psychologist believes
that these attitudes have changed over time. To test this he
randomly selects 230 individuals and asks them the same questions.
Can the psychologist confirm his theory that the attitudes have
changed from the first survey to the second survey? Attitude 1st
Survey 2nd Survey Optimistic 35%, 38% Slightly Optimistic 12%, 14%
Slightly Pessimistic...

A psychologist conducted a survey of the attitude towards the
sustainability of American energy consumption with 380 randomly
selected individuals several years ago. The psychologist believes
that these attitudes have changed over time. To test this he
randomly selects 380 individuals and asks them the same questions.
Can the psychologist confirm his theory that the attitudes have
changed from the first survey to the second survey?
Attitude
1st Survey
2nd Survey
Optimistic
6%
1%
Slightly Optimistic
29%
30%
Slightly Pessimistic...

A psychologist conducted a survey of the attitude towards the
sustainability of American energy consumption with 380380 randomly
selected individuals several years ago. The psychologist believes
that these attitudes have changed over time. To test this he
randomly selects 380380 individuals and asks them the same
questions. Can the psychologist confirm his theory that the
attitudes have changed from the first survey to the second
survey?
Attitude 1st Survey 2nd Survey
Optimistic 0.23 0.16
Slightly Optimistic 0.17 0.19
Slightly Pessimistic ...

A psychologist conducted a survey of the attitude towards the
sustainability of American energy consumption with 380 randomly
selected individuals several years ago. The psychologist believes
that these attitudes have changed over time. To test this he
randomly selects 380 individuals and asks them the same questions.
Can the psychologist confirm his theory that the attitudes have
changed from the first survey to the second survey? Attitude 1st
Survey 2nd Survey Optimistic 0.23 0.16 Slightly Optimistic 0.17
0.19 Slightly Pessimistic...

Managers rate employees according to job performance and
attitude. The results for several randomly selected employees are
given below.
Performance (x) / 3 / 4 / 8 / 1 / 10 / 5 / 9 / 2 / 3 / 10
Attitude (y) / 7 / 6 / 2 / 6 / 7 / 3 / 3 / 8 / 7 / 8
Use the given data to find the test statistic for testing linear
correlation. Round the final values...

Managers rate employees according to job performance and
attitude. The results for several randomly selected employees are
given below.
Performance (x) / 3 / 4 / 8 / 1 / 10 / 5 / 9 / 2 / 3 /
10
Attitude (y) / 7 / 6 / 2 / 6 / 7 / 3 / 3 / 8 / 7 / 8
Use the given data to find the test statistic for testing
linear correlation. Round the final values...

Managers rate employees according to job performance and
attitude. The results for several randomly selected employees are
given below.
Performance (x) / 5 / 3 / 3 / 7 / 6 / 9 / 9 / 7 / 3 / 8
Attitude (y) / 1 / 3 / 10 / 4 / 4 / 3 / 4 / 6 / 9 / 10
Use the given data to find the test statistic for testing linear
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A Gallup poll to survey the top concerns of Americans was
conducted. Suppose that 366366 women and 422422 men were
independently and randomly selected, and that 202202 women and
186186 men chose the state of the economy as their biggest concern.
Can we conclude that the proportion of women ( p1p1 ), choosing the
state of the economy as their biggest concern, exceeds the
proportion of men ( p2p2 )? Use a significance level of
α=0.05α=0.05 for the test.
Step 1...

A Gallup poll to survey the top concerns of Americans was
conducted. Suppose that 713 women and 613 men were independently
and randomly selected, and that 338 women and 244 men chose the
state of the economy as their biggest concern. Can we conclude that
the proportion of women ( p1 ), choosing the state of the economy
as their biggest concern, exceeds the proportion of men ( p2
)? Use a significance level of α=0.1 for the test.
Step 1...

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