You are interested in the difference between two population means. Both populations are normally distributed, and the population variances σ1212 and σ2222 are known. You use an independent samples experiment to provide the data for your study. What is the appropriate test statistic? t = x̄Dx̄D/ √[sD2sD2(1/n1n1 + 1/n2n2)]   F = s1s1/s2s2   z = (x̄1x̄1 – x̄2x̄2) / √[σ1212/n1n1 + σ2222/n2n2]   t = (x̄1x̄1 – x̄2x̄2) / √[sp2sp2(1/n1n1 + 1/n2n2)]     Suppose instead that the populations are not normally distributed. The test statistic given is still appropriate provided that    .   You are interested in the difference between two population means. The population variances σ1212 and σ2222 are unknown and equal. You use an independent samples experiment to generate the data for your study, and each of your samples meet the large sample requirement. What is the appropriate test statistic? z = (x̄1x̄1 – x̄2x̄2) / √[σ1212/n1n1 + σ2222/n2n2]   t = x̄Dx̄D/√[sD2sD2/nDnD]   F = s1s1/s2s2   t = (x̄1x̄1 – x̄2x̄2) / √[sp2sp2(1/n1n1 + 1/n2n2)]     Suppose instead that one (or both) of your samples does not satisfy the large sample requirement. The test statistic given is still appropriate provided that    .   You are interested in the difference between two population means. When is it appropriate to conduct a hypothesis test using the test statistic t = (x̄1x̄1 – x̄2x̄2) / √[s12s12/n1n1 + s22s22/n2n2]? Check all that apply. The populations are both normally distributed, the population variances σ1212 and σ2222 are unknown and unequal, and the data are generated from an independent samples experiment.   The population variances σ1212 and σ2222 are known, the data are generated from an independent samples experiment, and both populations are normally distributed.   The population variances σ1212 and σ2222 are unknown, the data are generated from a matched pairs experiment, and the population of differences are normally distributed.   The population variances σ1212 and σ2222 are unknown and equal, the data are generated from an independent samples experiment, and both populations are normally distributed.     You want to compare the two population variances σ1212 and σ2222. When is it appropriate to conduct a hypothesis test using the test statistic F = s12s12/s22s22? Check all that apply. The population variances σ1212 and σ2222 are known, and you independently sample from two normal populations.   The population variances σ1212 and σ2222 are unknown, and you independently sample from two normal populations.   The population variances σ1212 and σ2222 are unknown, the samples are not independent, and both populations are normally distributed.   The population variances σ1212 and σ2222 are unknown, and you independently sample from two nonnormal populations.     You are interested in comparing the central location of two populations whose data are measured on an interval scale. Your null hypothesis is that the population parameters are equal. The sample data are gathered from a matched pairs experiment. The population of differences is normally distributed. What is the appropriate test statistic? z = (p̂1p̂1 – p̂2p̂2) / √[p̂(1 – p̂)(1/n1+1/n2)√[p̂(1 – p̂)⁡1/n1+1/n2 ]   F = s12s12/s22s22   t = (x̄1x̄1 – x̄2x̄2) / √[sp2sp2(1/n1n1+1/n2n2)]   t = x̄Dx̄D / (sDsD/√nDnD)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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You are interested in the difference between two population means. Both populations are normally distributed, and the population variances σ1212 and σ2222 are known. You use an independent samples experiment to provide the data for your study. What is the appropriate test statistic?
t = x̄Dx̄D/ √[sD2sD2(1/n1n1 + 1/n2n2)]
 
F = s1s1/s2s2
 
z = (x̄1x̄1 – x̄2x̄2) / √[σ1212/n1n1 + σ2222/n2n2]
 
t = (x̄1x̄1 – x̄2x̄2) / √[sp2sp2(1/n1n1 + 1/n2n2)]
 
 
Suppose instead that the populations are not normally distributed. The test statistic given is still appropriate provided that    .
 
You are interested in the difference between two population means. The population variances σ1212 and σ2222 are unknown and equal. You use an independent samples experiment to generate the data for your study, and each of your samples meet the large sample requirement. What is the appropriate test statistic?
z = (x̄1x̄1 – x̄2x̄2) / √[σ1212/n1n1 + σ2222/n2n2]
 
t = x̄Dx̄D/√[sD2sD2/nDnD]
 
F = s1s1/s2s2
 
t = (x̄1x̄1 – x̄2x̄2) / √[sp2sp2(1/n1n1 + 1/n2n2)]
 
 
Suppose instead that one (or both) of your samples does not satisfy the large sample requirement. The test statistic given is still appropriate provided that    .
 
You are interested in the difference between two population means. When is it appropriate to conduct a hypothesis test using the test statistic t = (x̄1x̄1 – x̄2x̄2) / √[s12s12/n1n1 + s22s22/n2n2]? Check all that apply.
The populations are both normally distributed, the population variances σ1212 and σ2222 are unknown and unequal, and the data are generated from an independent samples experiment.
 
The population variances σ1212 and σ2222 are known, the data are generated from an independent samples experiment, and both populations are normally distributed.
 
The population variances σ1212 and σ2222 are unknown, the data are generated from a matched pairs experiment, and the population of differences are normally distributed.
 
The population variances σ1212 and σ2222 are unknown and equal, the data are generated from an independent samples experiment, and both populations are normally distributed.
 
 
You want to compare the two population variances σ1212 and σ2222.
When is it appropriate to conduct a hypothesis test using the test statistic F = s12s12/s22s22? Check all that apply.
The population variances σ1212 and σ2222 are known, and you independently sample from two normal populations.
 
The population variances σ1212 and σ2222 are unknown, and you independently sample from two normal populations.
 
The population variances σ1212 and σ2222 are unknown, the samples are not independent, and both populations are normally distributed.
 
The population variances σ1212 and σ2222 are unknown, and you independently sample from two nonnormal populations.
 
 
You are interested in comparing the central location of two populations whose data are measured on an interval scale. Your null hypothesis is that the population parameters are equal. The sample data are gathered from a matched pairs experiment. The population of differences is normally distributed. What is the appropriate test statistic?
z = (p̂1p̂1 – p̂2p̂2) / √[p̂(1 – p̂)(1/n1+1/n2)√[p̂(1 – p̂)⁡1/n1+1/n2 ]
 
F = s12s12/s22s22
 
t = (x̄1x̄1 – x̄2x̄2) / √[sp2sp2(1/n1n1+1/n2n2)]
 
t = x̄Dx̄D / (sDsD/√nDnD)
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