Aschool counselor tests whether the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at her school. on the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. reports on past testing indicate that fourth graders at her school usually score 5 on the scale, but the variation is not known. her sample of 20 fourth graders has a mean depression score of 4.4. the counselor tests the null hypothesis that fourth graders in this class do not differ from fourth graders in general at the school in level of depression. she calculated a t score of -.20. using the .05 significance level, what decision should she make regarding the null hypothesis?

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. here are data on the "penetrability" of the same type of soil at two levels of compression. penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil. compressed soil 2.85 2.66 3 2.82 2.76 2.81 2.78 3.08 2.94 2.86 3.08 2.82 2.78 2.98 3.00 2.78 2.96 2.90 3.18 3.16 intermediate soil 3.17 3.37 3.1 3.40 3.38 3.14 3.18 3.26 2.96 3.02 3.54 3.36 3.18 3.12 3.86 2.92 3.46 3.44 3.62 4.26 use the data, omitting the high outlier, to give a 95% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. compute degrees of freedom using the conservative method. interval: to