Fifteen years ago 57% of american families had money invested in the stock market. it is believed that this percentage has dropped. to see if this is true, morningstar recently sampled 200 american families and recorded in excel each family’s yes/no answer to the question "do you have money invested in the stock market? ". based on these results, can morningstar declare that the proportion of american families who have money invested in the stock market is now lower than .57 at α=.01? use the excel output above to answer the following question. find the critical value (typically two decimals if zcrit, three decimals if tcrit).

z(critic) = -2.33

Step-by-step explanation:

In this case this is a population proportion test because the observations are simple random sampled and there is a fixed number of trials with only two possible options. Also, n is big enough.

Since this is a population test, the test statistic is z.

Also, this is a one tailed tast because the claim is that the population proportion is less than 0.57.

In this case, for a 0.01 significance level, z(critic) = -2.33

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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