Question

11 . Choosing the appropriate test statistic
You are interested in the difference between two population means. Both populations are normally distributed, and the population variances σ212 and σ222 are known. You use an independent samples experiment to provide the data for your study. What is the appropriate test statistic?
F = √[2/n1 + 2/n2]
F = s1/s2
z = (x̄1 – x̄2) / √[σ2/n1 + σ2/n2]
z = (p̂1 – p̂2) / √[p̂(1 – p̂)(1/n1 + 1/n2)]
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 σ212 and σ222 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?
F =√[s21/n1 + s22/n2]
z = (p̂1 – p̂2) / √[p̂(1 – p̂)(1/n1 + 1/n2)]
t = (x̄1 – x̄2) / √[2(1/n1 + 1/n2)]
F = s1/s2
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) / √[2s12/n1n1 + 2s22/n2n2]? Check all that apply.
The population variances σ2 and σ2 are unknown, the data are generated from a matched pairs experiment, and the population of differences are normally distributed.
The populations are both normally distributed, the population variances σ2 and σ2 are unknown and unequal, and the data are generated from an independent samples experiment.
The population variances σ2 and σ2 are known, the data are generated from an independent samples experiment, and both populations are normally distributed.
The population variances σ2 and σ2 are unknown and equal, the data are generated from an independent samples experiment, and both populations are normally distributed.
You want to compar

Answer 1

A11.

1. c. z = (x̄1 – x̄2) / √[σ2/n1 + σ2/n2]

2. c. t = (x̄1 – x̄2) / √[2(1/n1 + 1/n2)]

3. a. The population variances σ2 and σ2 are unknown, the data are generated from a matched pairs experiment, and the population of differences are normally distributed.

b. The populations are both normally distributed, the population variances σ2 and σ2 are unknown and unequal, and the data are generated from an independent samples experiment.

d. The population variances σ2 and σ2 are unknown and equal, the data are generated from an independent samples experiment, and both populations are normally distributed.