# Two Sample Tes

Pages: 6 (864 words) Published: October 5, 2010
A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level.|

H0: µ1 ≤ µ2|
H1: µ1 > µ2|

(a)| Is this a one-tailed or a two-tailed test?|

This a one -tailed test.|

(b)| State the decision rule. (Round your answer to 2 decimal places.)|
The decision rule is to reject H0 if z greater than .|
(c)| Compute the value of the test statistic. (Round your answer to 2 decimal places.)|
The test statistic is z |

(d)| What is your decision regarding H0 ?|

H0 is| Not rejected.  |

(e)| What is the p-value? (Round your answer to 4 decimal places.)|
The p-value is|  |

Explanation:
(c)
| 0.607 found by|
| |

(e)
| p = 0.2709, found by 0.5000 - 0.2291|

A sample of scores on an examination given in Statistics 201 are:|

Men| 72| 69| 98| 66| 85| 76| 79| 80| 77|
-------------------------------------------------
Women| ------------------------------------------------- 81| -------------------------------------------------
67| -------------------------------------------------
90| -------------------------------------------------
78| -------------------------------------------------
81| -------------------------------------------------
80| -------------------------------------------------
76| -------------------------------------------------
| -------------------------------------------------
|

Hint: For the calculations, assume the women as the first sample. (1)| State the decision rule for .01 significance level: H0: μf ≤ μm ; H1: μf> μm. (Round your answer to 3 decimal places.)|

Reject H0 if t >|  |

(2)| Compute the value of the test statistic. (Round your answer to 3 decimal places.)|

Value of the test statistic|  |

(3)| At the .01 significance level, is the mean grade of the women higher than that of the men?|

Fail to reject H0. The mean grade of the women is not higher than that of the   men.|

Explanation:
(1)
| df = 9 + 7 – 2 = 14|
| Reject H0 if t > 2.624|
(2)|  |
| |
|  |
| |
(3)|  |
| Do not reject H0. There is higher in the mean grades.|

In a poll recently conducted at Iowa State University, 68 out of 98 male students and 45 out of 85 female students expressed “at least some support” for implementing regulations to limit greenhouse gases.|

(1)| State the decision rule for .05 significance level: H0: πm = πf; H1: πm ≠ πf. (Negative amount should be indicated by a minus sign.Round your answer to 2 decimal places.)|

Reject H0 if z < to or z > |

(2)| Compute the value of the test statistic. (Round your answer to 2 decimal places.)|

Value of the test statistic|  |

(3)| What is your decision regarding the null hypothesis that the population proportions are equal against the two-tailed alternative? Use the 0.05 significance level.|

RejectH0. The population proportions are not the same.|

Explanation:
(2)

the Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three others were sprayed with Action. When the grapes ripened, 400 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 400 vines sprayed with Action were checked. The results are:|

| Number of|  |
| Vines...