Question

Sony would like to test the hypothesis that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users. the following table summarizes sample statistics from each population.

PlayStation | Xbox | |

Sample Standard Deviation | 4.3 years | 3.9 years |

Sample size | 25 | 28 |

using a= 0.05, the conclusion for this hypothesis test would be that because the test statistics is

A) more than the critical value, we reject the null hypothesis and cannot conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.

B) less than the critical value, we fail to reject the null hypothesis and conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.

C) less than the critical value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.

D) more than the critical value, we fail to reject the null hypothesis and conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.

Answer #1

**Option C is correct.**

Playstation | Xbox | |

Sample standard deviation | 4.3 | 3.9 |

Sample size | 25 | 28 |

F | 1.2156476 | |

Degree of freedom Numerator | 24 | |

Degree of freedom Denominator | 27 | |

Critical value | 1.92994028 | |

P-value | 0.31003244 |

Since F is less than critical value so we fail to reject the null hypothesis.

Since the test statistic is less than the critical value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.

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