Question

5. For a test of

H₀ : p = p₀

vs.

H₁ : p < p₀,

the value of the test statistic z _obs is -1.87. What is the p-value of the hypothesis test? (Express your answer as a decimal rounded to three decimal places.)

6. A pilot survey reveals that a certain population proportion p is likely close to 0.56. For a more thorough follow-up survey, it is desired for the margin of error to be no more than 0.03 (with 95% confidence). Assuming that the data from the pilot survey are reliable, what sample size is necessary to achieve this? (Express your answer as an integer, rounded as appropriate.)

7. Suppose that you are testing whether a coin is fair. The hypotheses for this test are

H₀: p = 0.5

and

H₁: p ≠ 0.5.

Which of the following would be a type I error?

	a	Concluding that the coin is fair when in reality the coin is not fair.
	b	Concluding that the coin is not fair when in reality the coin is fair.
	c	Concluding that the coin is fair when in reality the coin is fair.
	d	Concluding that the coin is not fair when in reality the coin is not fair.

8. For a two-sided hypothesis test in which the test statistic is z_obs, which of the following critical values is appropriate if a 10% significance level is desired?

a		1.645
b		1.960
c		2.326
d		2.576

Answer 1

5. this is a left tailed test

test statistic (z _obs) = -1.87.

the p-value of the hypothesis test is :-

[ using standard normal table]

6.given data are:-

margin of error (E) = 0.03

population proportion (p) = 0.56

z critical value for 95% confidence level, both tailed test be:-

the needed sample size be:-

7).the type I error is:-

Concluding that the coin is not fair when in reality the coin is fair. (b)

[ type 1 error is defined as, rejecting the null hypothesis, when it is actually true.]

8).

[ for alpha= 0.10 , both tailed test]

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