A marriage counselor has traditionally seen that the proportion p of all married couples for whom her communication program can prevent divorce is 75%. After making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than 75% of married couples. In a random sample of 230 married couples who completed her program, 190 of them stayed together. Based on this sample, is there enough evidence to support the marriage counselor's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho H₁ :0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Is there enough evidence to support the marriage counselor's claim that the proportion of married couples for whom her program can prevent divorce is more than 75%? O Yes O No H XI 0#0 a 0=0 OSO x S □<ロ Р Â S 00 020 O>O

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A grocery store has 6 self-checkout stations. The probability distribution of the number of utilized stations, XX, is as follows: xixi  1 2 3 4 5 6 Total P(X=xi)P(X=xi)  0.12 0.15 0.42 0.2 0.11 0 1 To find the expected value the following table was set up:  xixi   P(X=xi)P(X=xi)   xi⋅P(X=xi)xi⋅P(X=xi)  1 0.12  1⋅0.12=0.121⋅0.12=0.12  2    2⋅0.15=0.32⋅0.15=0.3  3 0.42  3⋅3⋅ =1.26=1.26  4 0.2  4⋅0.2=4⋅0.2=  5    5⋅0.11=0.555⋅0.11=0.55   6 0       Total:   Fill out the blanks in the table above and compute the E[X]:  E[X]=E[X]=  (Round the answer to 2 decimals)

- 2.a O 2.60

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