For each question, provide a written response.Forfull credit,please show your workfor all calculations androundto the second decimal place (e.g., 5.0365.04).

1. A professor is concerned that his exam questions are culturally biased, and that students who were not born in the United States are scoring worse than native students. To test this, he measures exam grades from this section of material among a sample of his U.S. born students (n = 10) and international students (n = 10). The mean score in the U.S. born group was 84 with a SS of 144; in the international student group,the mean was 78 and the SS was 576. If the null hypothesis is that there is no difference in exam scores, then test the null hypothesis using a two-tailed test with a Type I error rate of .05.

a. (1 points) Which statistical test you should use? Explain why.

b. (2 point) State the null and alternative hypotheses both in words and using statistical notation

c. (1 point) Provide thet_crit and df values.

d. (2 points)Compute the test statistic

e. (1 point)Make a decision.

f. (1 point) Compute the 95% confidence interval for the mean difference of exam scores