Question

A SAMPLE OF 300 CUSTOMERS WAS DRAWN FOR A POLL OF THEIR SATISFACTION WITH THE NEW SERVICE AGREEMENT. IT TURNED OUT THAT 212 WERE SATISFIED.

(A) AT THE 5% SIGNIFICANCE LEVEL, DO WE HAVE SUFFICIENT EVIDENCE THAT THE POPULATION SATISFACTION RATE WAS BELOW 75%?

CIRCLE APPROPRIATE ANSWER: YES! NO!

(B) SHOW THE TEST STATISTIC VALUE, THE CRITICAL VALUE(S) NEEDED FOR YOUR DECISION AND FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES...

(C) AT THE 5% SIGNIFICANCE LEVEL, DO WE HAVE SUFFICIENT EVIDENCE THAT THE POPULATION SATISFACTION RATE DIFFERS FROM 75%? CIRCLE APPROPRIATE ANSWER: YES! NO!

(D) SHOW THE CRITICAL VALUE(S) NEEDED FOR YOUR DECISION AND FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES...

Answer 1

= 212/300 = 0.7067

p = 0.75 and 1 - p = 0.25

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(A) At the 5% significance level, do we have sufficient evidence that the population rate was below 75% - YES

(B) The Hypothesis:

H0: p = 0.75

Ha: p < 0.75

The Test Statistic:

The Critical Values: The critical value (Left tail), at = 0.05, is -1.645.

The Rejection Rule: States that, If Z test is < - Zcritical, then Reject H0.

The Decision: Since Z test(-1.73) is < -Zcritical (-1.645), We Reject H0.

The Conclusion: Yes, there is suffcient evidence at the 95% significance level to conclude that the population satisfaction rate is below 75%.

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(C) At the 5% significance level, do we have sufficient evidence that the population rate was different from 75% - NO

(B) The Hypothesis:

H0: p = 0.75

Ha: p 0.75

The Test Statistic:

The Critical Values: The critical value (Two tails), at = 0.05, is +1.96 and-1.96.

The Rejection Rule: States that, If Z test is < - Zcritical or if Ztest is > Z critical, then Reject H0.

The Decision: Since Z test(-1.73) is in between the 2 critical values -1.96 and +1.96, We Fail to Reject H0.

The Conclusion: No, there is insuffcient evidence at the 95% significance level to conclude that the population satisfaction rate is different from 75%.

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