In: Statistics and Probability

A fitness trainer is interested in investigating whether ethnicity and the first exercise activity that members engage in are dependent. The table below shows the results of the trainer's observation of randomly selected members. Frequencies of Ethnicity and Exercise Activity Cardio Weight Machines Free Weights White 88 82 88 Hispanic 86 82 95 Black 44 57 63 Other 60 41 48 What can be concluded at the alpha = 0.01 significance level? What is the correct statistical test to use? Homogeneity Independence Goodness-of-Fit Paired t-test What are the null and alternative hypotheses? H_0: The distribution of first exercise activity is the same for each ethnicity. Ethnicity and first exercise activity are independent. Ethnicity and first exercise activity are dependent. The distribution of first exercise activity is not the same for each ethnicity. H_1: Ethnicity and first exercise activity are independent. The distribution of first exercise activity is not the same for each ethnicity. Ethnicity and first exercise activity are dependent. The distribution of first exercise activity is the same for each ethnicity. The test-statistic for this data = (Please show your answer to three decimal places.) The p-value for this sample = (Please show your answer to four decimal places.) The p-value is alpha Based on this, we should accept the null fail to reject the null reject the null Thus, the final conclusion is... There is sufficient evidence to conclude that the distribution of first exercise activity is not the same for each ethnicity. There is sufficient evidence to conclude that ethnicity and first exercise activity are independent. There is insufficient evidence to conclude that the distribution of first exercise activity is not the same for each ethnicity. There is insufficient evidence to conclude that ethnicity and first exercise activity are dependent. There is sufficient evidence to conclude that ethnicity and first exercise activity are dependent.

correct statistical test to use? Independence

Ho:Ethnicity and first exercise activity are independent

H1: Ethnicity and first exercise activity are dependent.

Applying chi square test:

Expected |
E_{i}=row total*column
total/grand total |
cardio | weight m/c | free weights | Total |

white | 86.00 | 81.05 | 90.95 | 258 | |

Hispanic | 87.67 | 82.62 | 92.71 | 263 | |

Black | 54.67 | 51.52 | 57.81 | 164 | |

other | 49.67 | 46.81 | 52.53 | 149 | |

total | 278 | 262 | 294 | 834 | |

chi square χ^{2} |
=(O_{i}-E_{i})^{2}/E_{i} |
cardio | weight m/c | free weights | Total |

white | 0.0465 | 0.0111 | 0.0957 | 0.153 | |

Hispanic | 0.0317 | 0.0047 | 0.0565 | 0.093 | |

Black | 2.0813 | 0.5828 | 0.4654 | 3.129 | |

other | 2.1499 | 0.7207 | 0.3899 | 3.260 | |

total | 4.309 | 1.319 | 1.007 | 6.6360 |

The test-statistic for this data =6.636

The p-value for this sample = 0.3558

fail to reject the null

There is insufficient evidence to conclude that ethnicity and first exercise activity are dependent

A fitness trainer is interested in investigating whether
ethnicity and the first exercise activity that members engage in
are dependent. The table below shows the results of the trainer's
observation of randomly selected members.
Frequencies of Ethnicity and Exercise Activity
CardioWeight MachinesFree Weights
White849487
Hispanic868887
Black525351
Other656857
What can be concluded at the = 0.01 significance
level?
What is the correct statistical test to use?
Independence
Paired t-test
Homogeneity
Goodness-of-Fit
What are the null and alternative hypotheses?
Ethnicity and first exercise...

A fitness trainer is interested in investigating whether
ethnicity and the first exercise activity that members engage in
are dependent. The table below shows the results of the trainer's
observation of randomly selected members.
What can be concluded at the 0.05 level of significance?
Cardio
Weight
Machines
Free Weights
White
87
52
55
Hispanic
41
20
17
Black
36
19
11
Other
28
16
7
Helpful Video (Links to an external site.)
Hint (Links to an external site.)
Textbook Pages...

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х= 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8

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whether there is a gender bias in the workplace. Specifically, they
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Suppose the sales team at Apple is interested in investigating
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Frequencies of Living Situation and Pet
SingleFamilyCouple
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Various444342
None685942
What can be concluded at the αα = 0.05 significance level?
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You are interested in investigating whether gender and major are
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Frequencies of Majors and
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Math/Science
Arts/Humanities
Business/Econ.
Other
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100
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Women
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What can be concluded at the αα = 0.01 significance level?
What is the correct statistical test to use?
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Homogeneity
Paired t-test
Goodness-of-Fit
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