3. Consider each of the following scenarios, and choose the statistical pro- ced

Question

3. Consider each of the following scenarios, and choose the statistical pro- cedure from the bottom of the page that appears to be most suitable for assessing the difference in population means under the given scenario. If you are uncertain, write ONE sentence explaining your uncertainty (a) Data are sampled from two Normal populations with different standard deviations. The sample size of the sample with the larger standard deviation is 50, and the sample size of the other sample is 20 (b) A pumpkin grower wants to determine which variety of pumpkins pro- duces more fruit per vine. She randomly selects 20 vines from variety A and 20 vines from variety B. For each vine, she counts the number of pumpkins that weigh 2 or more pounds variable . This count is he r response (c) A social scientist is interested in whether newly married couples want to have the same number of children. She sampled 12 couples and asked each partner how many children he/she would like to have. The responses are the number of children desired by each member of the cou (d) Samples are taken from two populations, both of which are skewed towards higher values. The variance of the sample with the lower center appears to be slightly smaller than that of the other sample. ed t-test rank-sum test two-sample t-test pair signed-rank test randomization test Levene's test one-sample t-test Welch's t-test sign test permutation test two-sample t-test on log-scale data

Explanation / Answer

a) Welch's t-test because it is a two-sample location test which is used to test the hypothesis that two populations have equal means. Welch's t-test is an adaptation of Student's t-test, that is more reliable when the two samples have unequal variances and unequal sample sizes.

b) Rank-sum test because it is used to investigate if two random samples could have come from two population with the same mean. (Parametric assumptions are not met here)

c) Signed-rank test because it is used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test, t-test for matched pairs, or the t-test for dependent samples when the population cannot be assumed to be normally distributed.

d) Uncertain because there is not much information about the means of two samples.

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