Question

Amara was working on a report on Greek and Egyptian mathematicians. She decided to find a 98 percent confidence interval for the difference in mean age at the time of significant mathematics discoveries for Greek versus Egyptian mathematicians. She found the ages at the time of math discovery of all the members of both groups and found the 98 percent confidence interval based on a t-distribution using a calculator.

The procedure she used is not appropriate in this context becauseA. The sample sizes for the two groups are not equal.B. Age at the time of math discovery occurs at different intervals in the two countries, so the distribution of ages cannot be the same.C. Ages at the time of math discovery are likely to be skewed rather than bell shaped, so the assumptions for using this confidence interval formula are not valid.D. Age at the time of math discovery is likely to have a few large outliers, so the assumption for using this confidence interval formula is not valid.E. The entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.

Answer 1

E. The entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.

Explanation:

The entire population of Greek and Egyptian mathematicians was already measured by Amara. She can measure the actual difference in the mean. Therefore, she needn't use a confidence interval. It is mostly common for a researcher to be more interested in the difference between means than in the specific values of the means. The difference in sample means is used to compute the difference in population means.

Amara's sample is a random selection of Greek and Egyptian mathematicians. It is a smaller group drawn from the population that has the characteristics of the entire population. The observations and conclusions made against the sample data are attributed to the population. In this case, the entire position is measured.

A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups (Greek and Egyptian mathematicians) which may be related in certain features. It is mostly used when the data sets, like the data set recorded as the outcome from rolling a die 50 times, would follow a normal distribution and may have unknown variances. A t-test is used as a hypothesis testing tool, which allows testing of an assumption applicable to a population. Once the actual difference is known, a confidence interval should not be used.