Professor Good man claims that 50% of his students in a large class achieve a fi

Question

Professor Good man claims that 50% of his students in a large class achieve a final score 90 points or higher. A student asks 12 randomly selected student from Professor Goodman's class and they report the following scores. 80 81 87 94 79 78 89 92 89 90 88 79 To test at 0.05 significance level that Professor Goodman's claim is not consistent with the evidence, what is the rejection region? T greaterthanorequalto 10 T lessthanorequalto 2 or T greaterthanorequalto 9 T lessthanorequalto 2 or T greaterthanorequalto 10 T lessthanorequalto 1 or T greaterthanorequalto 10 T lessthanorequalto 2

Explanation / Answer

H0: p = 0.50

Ha : p 0.50

There are 12 students in the sample and confidence level is 0.05.

As the test is non-directional as we have to just collect evidence against the professor's claim that 50% of his students scored 90 percent or higher.

Number of students who got 90 or higher 90 marks = 3

NUmber of students who got less than 90 marks = 9

for smaller sample

critical value lower value = BIN (T; n=12; 0.5) <= 0.025

where BIN is the cumulative distribution

T = 2

for lower value => BIN(T ; n= 12; 0.5) >= 0.975

T = 10

so We will reject the claim when T <=2 and T>=10

so option C is correct.

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