Hypothesis: Standard Deviation and Critical Value

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Study Guide - Testing the Difference Between Two Means, Two Variances, and Two Proportions

1.|If the test value in the figure below is 2.57 when the critical value is 1.96, what decision about the hypothesis should be made?| A)|reject the null hypothesis |
B)|accept the null hypothesis |
C)|reject the alternative hypothesis |
D)|not enough information |

2.|The standard error of difference is .|
A)|True|
B)|False|

3.|In the figure below, if the -test value is 1.43, the null hypothesis should not be rejected. | A)|True|
B)|False|

4.|When hypothesizing a difference of 0, if the confidence interval does not contain 0, the null hypothesis is rejected.| A)|True|
B)|False|

5.|For normally distributed populations, if the samples are independent and the variances are known, the -test is used.| A)|True|
B)|False|

Use the following to answer questions 6-8:

A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below.

|Africa|Asia|
|55.3|65.2|
|8.1|9.3|
|53|42|

6.|What is the null hypothesis? Use .|
A)| |
B)| |
C)| |
D)| |

7.|Calculate the critical value. Use .|
A)|–1.65 |
B)|–2.33 |
C)|–2.58 |
D)|–1.96 |

8.|What is the test value? Use .|
A)|–6.86 |
B)|–3.70 |
C)|–4.13 |
D)|–5.45 |

9.|Determine the 95% confidence interval of the true difference in the means. A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Use .|Africa|Asia| |55.3|65.2| |8.1|9.3| |53|42|| A)| |

B)| |
C)| |
D)| |

10.|The formula for the -test for comparing two means from independent populations is __________.|

11.|Joan moves into her new apartment and wants to purchase a new couch. She wants to determine if there is any difference between the average costs of couches at two different stores. Test the hypothesis that there is no difference at .|Store 1|Store 2| |$650|$730| |$61|$78| |24|21||

12.|A conservationist wants to know if the average water level in Horseshoe Lake is more than the average water level in Swan Lake. Test his hypothesis at .|Horseshoe Lake|Swan Lake| |43|38| |3.2|2.4| |23|23||

13.|The value of cannot be negative, because variances are always positive or zero.| A)|True|
B)|False|

14.|When finding the -test value, the smaller of the variances is placed in the numerator.| A)|True|
B)|False|

15.|When comparing two variances or standard deviations, a -test is used.| A)|True|
B)|False|

16.|The critical value for a one-tailed right -test is 2.57, when , the degrees of freedom for the numerator = 15, and the degrees of freedom for the denominator = 20.| A)|True|
B)|False|

17.|The critical value for a two-tailed -test is 2.65, when , the sample size from which the variance for the numerator was obtained = 10, and the sample size from which the variance for the denominator was obtained = 15.| A)|True|

B)|False|

18.|The mean value of is approximately equal to __________.|

19.|To determine whether two sample variances are equal, a researcher can use a(n) __________.|

20.|If and , what is the value of as shown in the figure below?| A)|5.78 |
B)|8.43 |
C)|71.14 |
D)|17.97 |

21.|What is the critical value for a two-tailed -test with , when the sample size from which the variance for the numerator was obtained was 10, and the sample size from which the denominator was obtained was 24? | A)|2.27 |

B)|2.25 |
C)|2.32 |
D)|2.30 |

22.|Compute the critical value for a right-tailed -test with , d.f.N. = 21, and d.f.D. = 20. | A)|2.12 |
B)|2.23 |
C)|2.20 |
D)|2.16 |

23.|A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons. The standard deviation of 16 convertibles is $6800...
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