A random sample of *n*_{1} = 16 communities in western Kansas gave the following information for people under 25 years of age.

97 | 91 | 122 | 130 | 94 | 123 | 112 | 93 |

125 | 95 | 125 | 117 | 97 | 122 | 127 | 88 |

A random sample of *n*_{2} = 14 regions in western Kansas gave the following information for people over 50 years old.

94 | 111 | 100 | 95 | 110 | 88 | 110 |

79 | 115 | 100 | 89 | 114 | 85 | 96 |

(i) Use a calculator to calculate x_{1}, *s*_{1}, x_{2}, and *s*_{2}. (Round your answers to four decimal places.)

x_{1} |
= |

s_{1} |
= |

x_{2} |
= |

s_{2} |
= |

A random sample of *n*_{1} = 16 communities in western Kansas gave the following information for people under 25 years of age.

97 | 91 | 122 | 130 | 94 | 123 | 112 | 93 |

125 | 95 | 125 | 117 | 97 | 122 | 127 | 88 |

A random sample of *n*_{2} = 14 regions in western Kansas gave the following information for people over 50 years old.

94 | 111 | 100 | 95 | 110 | 88 | 110 |

79 | 115 | 100 | 89 | 114 | 85 | 96 |

What is the value of the sample test statistic? (Test the difference μ_{1} − μ_{2}. Round your answer to three decimal places.)

A random sample of *n*_{1} = 16 communities in western Kansas gave the following information for people under 25 years of age.

100 | 92 | 122 | 127 | 93 | 123 | 112 | 93 |

125 | 95 | 125 | 117 | 97 | 122 | 127 | 88 |

A random sample of *n*_{2} = 14 regions in western Kansas gave the following information for people over 50 years old.

93 | 112 | 100 | 97 | 111 | 88 | 110 |

79 | 115 | 100 | 89 | 114 | 85 | 96 |

State the null and alternate hypotheses.

What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student’s *t*. We assume that both population distributions are approximately normal with known standard deviations.

The Student’s *t*. We assume that both population distributions are approximately normal with unknown standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

What is the value of the sample test statistic? (Test the difference ?_{1} − ?_{2}. Round your answer to three decimal places.)

Find (or estimate) the *P*-value.

0.125 < *P*-value < 0.250

0.050 < *P*-value < 0.125

0.025 < *P*-value < 0.050

0.005 < *P*-value < 0.025

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.

Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.

Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.

Fail to reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.

*n*_{1} = 16 communities in western Kansas gave the following information for people under 25 years of age.

100 | 92 | 121 | 129 | 93 | 123 | 112 | 93 |

125 | 95 | 125 | 117 | 97 | 122 | 127 | 88 |

*n*_{2} = 14 regions in western Kansas gave the following information for people over 50 years old.

93 | 108 | 103 | 98 | 112 | 88 | 110 |

79 | 115 | 100 | 89 | 114 | 85 | 96 |

(i) Use a calculator to calculate x_{1}, *s*_{1}, x_{2}, and *s*_{2}. (Round your answers to four decimal places.)

x_{1} |
= |

s_{1} |
= |

x_{2} |
= |

s_{2} |
= |

What is the value of the sample test statistic? (Test the difference μ_{1} − μ_{2}. Round your answer to three decimal places.)

A random sample of *n*_{1} = 16 communities in western Kansas gave the following information for people under 25 years of age.

100 | 92 | 121 | 129 | 93 | 123 | 112 | 93 |

125 | 95 | 125 | 117 | 97 | 122 | 127 | 88 |

*n*_{2} = 14 regions in western Kansas gave the following information for people over 50 years old.

93 | 108 | 103 | 98 | 112 | 88 | 110 |

79 | 115 | 100 | 89 | 114 | 85 | 96 |

(c) Find (or estimate) the *P*-value.

0.125 < *P*-value < 0.250

0.050 < *P*-value < 0.125

0.025 <*P*-value < 0.050

0.005 < *P*-value < 0.025

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant

.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.

Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.

Fail to reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.

Fail to reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.

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