Question 1087841: A scientist claims that only 65% of geese in his area fly south for the winter. He tags 55 random geese in the summer and finds that 17 of them do not fly south in the winter. If = .05, is the scientist's belief warranted? (Hint: Z test of proportion)
Yes, because the test value 0.64 is in the noncritical region.
No, because the test value 0.70 is in the critical region.
Yes, because the test value –0.70 is in the noncritical region.
No, because the test value –0.64 is in the noncritical region.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Ho: x = 0.65
H1: x not = 0.65
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This requires a two-tailed test
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Our significance level is 5% or 0.05
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The sample proportion = (55-17) / 55 = 0.6909 approx 0.69
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standard error(SE) = square root(0.69 * (1-0.69) / 55) = 0.0624
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z-value = (0.69 - 0.65) / 0.0624 = 0.641 approx 0.64
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The z statistic at 0.05 is -1.96 or 1.96 for a two tailed test
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Since our test statistic has a z value of 0.64, we do not reject Ho.
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answer is "Yes, because the test value 0.64 is in the noncritical region"
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that is 0.64 is less than 1.96
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