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A snowboarding competition site is using a new design for the parallel giant slalom. The designer of the slalom is investigating whether there is a difference in the mean times taken to complete a run for men and women competitors. As part of the investigation, independent random samples of men and women who will use the slalom run are selected and their times to complete a run are recorded. Which of the following is the appropriate inference procedure by which the designer can estimate the difference in the mean completion times for men and women?
i. A one-sample I-Interval for a sample mean e-sample interval for a population mean
ii. A matched para tantervil for a meen difference
iii. A two-sample -interval for a difference between population means
iv. A two-sample t-interval for a difference between sample means

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Answer:

Considering that we have two samples, and the standard deviation for each sample, the correct test is given by:

iii. A two-sample -interval for a difference between population means.

When to use a t-test and a z-test?

  • If we have the standard deviation for the sample, the t-test is used.
  • If we have the standard deviation for the population, a z-test is used.

Here, there are two samples, and we will investigate their difference. The information taken from the sample is expanded to the population, and since we have the standard deviation for each sample, a t-test is used, hence the correct option is given by:

iii. A two-sample -interval for a difference between population means.

More can be learned about hypothesis tests at

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