Question

Nine homes are chosen at random from real estate listings in two suburban neighborhoods, and the square footage of each home is noted in the following table.

Size of Homes in Two Subdivisions | |||||||||

Subdivision | Square Footage | ||||||||

Greenwood | 2,780 | 2,710 | 2,404 | 2,622 | 2,413 | 2,888 | 2,378 | 2,609 | 2,650 |

Pinewood | 2,484 | 2,356 | 2,453 | 2,759 | 2,631 | 2,672 | 2,373 | 2,511 | 3,093 |

**(a)** Choose the appropriate hypothesis to test
if there is a difference between the average sizes of homes in the
two neighborhoods at the .10 significance level. Assume
?_{1} is the mean of home sizes in Greenwood and
?_{2} is the mean of home sizes in Pinewood.

a. *H*_{0}: *?*_{1} –
*?*_{2} = 0 vs. *H*_{1}:
*?*_{1}– *?*_{2} ? 0

b. *H*_{0}: *?*_{1} –
*?*_{2} ? 0 vs. *H*_{1}:
*?*_{1}– *?*_{2} = 0

**(b)** Specify the decision rule with respect to
the *p*-value.

Reject the null hypothesis if the *p*-value is (Click to
select)greater thanless than 0.10.

**(c)** Find the test statistic
*t*_{calc}. **(A negative value should be
indicated by a minus sign. Round your answer to 3 decimal
places.)**

**(d)** Assume unequal variances to find the
*p*-value. **(Use the quick rule to determine degrees
of freedom. Round your answer to 4 decimal places.)**

*p*-value

**(e)** Make a decision.

We reject or do not reject the null hypothesis.

**(f)** State your conclusion.

We can or cannot conclude that there is a difference between the sizes of homes in the two neighborhoods.

Answer #1

(a)

Hypotheses are:

(b)

If p-value is less than 0.10 so we reject the null hypothesis.

(c)

Following is the output of descriptive statistics:

Descriptive statistics | ||

Greenwood | Pinewood | |

count | 9 | 9 |

mean | 2,606.00 | 2,592.44 |

sample standard deviation | 177.78 | 231.30 |

sample variance | 31,606.75 | 53,501.53 |

minimum | 2378 | 2356 |

maximum | 2888 | 3093 |

range | 510 | 737 |

So we have

The test statistics will be

(d)

Since it is not given that variances are equal so degree of freedom of the test is

So df is 8.

The test is two tailed so p-value is: 0.8929

(e)

Fail to reject the null hypothesis.

(f)

We cannot conclude that there is a difference between the sizes of homes in the two neighborhoods.

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