In which of the following scenarios will conducting a two-sample t-test for means be appropriate? Check all that apply.
A. To test if there is a difference between the proportion of low-income families in British Columbia and a known national proportion.
B. To test if the mean annual income of Ontarians is higher than that of British Columbians.
C. To test if there is a difference between the mean annual income of husbands and that of wives in Canada.
D. To test if the proportion of low-income families is higher than that of high-income families in British Columbia.
E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.
F. To test if there is a difference between the mean annual income of British Columbians and a known national mean.
G. None of the above

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Answer:

B. To test if the mean annual income of Ontarians is higher than that of British Columbians

E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.

Explanation:

The options chosen have two populations that are independent. For example in option B, the annual income of Ontarians is a different population from annual income of British Columbians and they are also independent. The two sample t test can only be used when the populations are independent, it can also be used when computing difference between the means of two populations

The scenarios where conducting a two-sample t-test for means be appropriate include:

  • A. To test if there is a difference between the proportion of low-income families in British Columbia and a known national proportion.
  • E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.

It should be noted that the two sample t-test is used when the populations are independent band the sample size is small.

Therefore, it will be appropriate to test if there is a difference between the proportion of low-income families in British Columbia and a known national and the difference between the mean annual income of male British Columbians and that of female British Columbians.

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