Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: , , , , , . Use a significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?

How many triangles can be drawn with side lengths 4 centimeters, 4.5 centimeters, and 9 centimeters? explain

If abcde is reflected over the x-axis and then translated 3 units left, what are the new coordinates d? are he re

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.