Question

3. Duolingo (a language learning mobile application) claims that app users who are also taking language classes will have a significantly larger vocabulary compared to people taking language classes who are not using Duolingo. Two independent samples of language learners (‘Duolingo+class’ (μ1), and ‘class only’ (μ2)) were sampled. Both groups were given a vocabulary test. Using an alpha of 0.025, determine whether there is a significant difference in vocabulary size between groups. The data are below. 
3a. State the null and alternative hypotheses (1 point)
3b. We will assume a pooled variance. What is the evidence that doing so is appropriate? (1 point)
3c. Calculate the test statistic for Q3a (3 points); and state your conclusion (1 point)

we had assumed equal variances.

3d). Statistically test whether this was appropriate to do so (with alpha of 5%). (1 point)

3e). Calculate the 95% confidence interval. Interpret the 95% confidence interval and how it relates to your hypothesis regarding equal variances. (3 points)

Answer 1