Formulate and test hypotheses to determine if statistical evidence suggests that the graduation rate for (1) top liberal arts colleges or (2) research universities in the accompanying table exceeds 90%. Do the data support a conclusion that the graduation rates exceed 85%? Would your conclusions change if the level of significance was 0.01 instead of 0.05?

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Top Liberal Arts Colleges Graduation % Research Universities Graduation % 92 68 78 92 89 76 90 76 86 89 82 81 74 93 84 88 84 89 87 84 73 87 83 82 86 94 92 89 85 88 75 78 70 73 79 74 86 86 89 89 83 59 79 71 87 78 90 94 91

Is there sufficient evidence at the 0.05 level of significance that the graduation rate for top liberal arts colleges exceeds 90%?Determine the null hypothesis,

HSubscript0,

and the alternative hypothesis,

HSubscript1.

HSubscript0:

mu

less than or equals

9090%

HSubscript1:

mu

greater than>

9090%

(Type integers or decimals. Do not round.)Part 2Compute the test statistic.

negative 5.045.04

(Round to two decimal places as needed.)Part 3Find the p-value for the test.

1.0001.000

(Round to three decimal places as needed.)Part 4State the conclusion.The p-value is

greater than

the chosen value of

alpha,

so

do not reject

the null hypothesis. There is

insufficient

evidence to conclude that the mean is greater than 90%.Part 5Is there sufficient evidence at the 0.05 level of significance that the graduation rate for top liberal arts colleges exceeds 85%?Determine the null hypothesis,

HSubscript0,

and the alternative hypothesis,

HSubscript1.

HSubscript0:

mu

less than or equals

8585%

HSubscript1:

mu

greater than>

8585%

(Type integers or decimals. Do not round.)Part 6Compute the test statistic.

negative 1.001.00

(Round to two decimal places as needed.)Part 7Find the p-value for the test.

enter your response here

(Round to three decimal places as needed.)