Question

**Difference between two population means (two independent samples).**The data on the estimated average price for a 6-ounce can of tuna, based on prices paid nationally in supermarkets, is available in the file “Tuna”. Two types of tuna are considered: light tuna in water and light tuna in oil. Test if the price of tuna in water is significantly less than the price of tuna in oil.

Light Water | Light Oil |

0.99 | 2.56 |

1.92 | 1.92 |

1.23 | 1.3 |

0.85 | 1.79 |

0.65 | 1.23 |

0.69 | 0.62 |

0.6 | 0.66 |

0.53 | 0.62 |

1.41 | 0.65 |

1.12 | 0.6 |

0.63 | 0.67 |

0.67 | |

0.6 | |

0.66 |

Using Minitab, generate output for this test. (Use α = 0.05)

- State the two hypotheses you are using in this test.
- What is the calculated test statistic? What is the critical value (using a T-table)? Draw a sketch of the rejection region.
- What is the p-value for the test?
- What can you conclude about the prices for different types of tuna based on the test? Discuss your conclusion.

Answer #1

From MINITAB output

a) The two hypothesis in the test is

b) The test statistics t = -1.16

c) P-value = 0.130

d) Given

then P-value = 0.130 > 005

so, fail to reject H_{0}

hence there is no evidence that the price of tuna in water is significantly less than the tuna in oil

The following data give the estimated prices of a 6-ounce can or
a 7.06-ounce pouch of water-packed tuna for 14 different brands,
based on prices paid nationally in supermarkets.
0.97
1.95
1.24
0.82
0.66
0.52
1.41
1.11
0.63
0.72
0.74
0.61
0.64
0.65
Find the range.
Find the sample variance. (Round your answer to four decimal
places.)
Find the sample standard deviation. (Round your answer to three
decimal places.)

In testing the difference between two population means using two
independent samples, the population standard deviations are assumed
to be unknown, each sample size is 30, and the calculated test
statistic z = 2.56. If the test is a two-tailed and the 5% level of
significance has been specified, the conclusion should be:
a.
none of these answers is correct.
b.
choose two other independent samples.
c.
reject the null hypothesis.
d.
not to reject the null hypothesis.

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