Question

1. Which of the following is a valid alternative hypothesis for a one-sided hypothesis test about a population proportion p?

	a	p = 0.6
	b	p > 0.3
	c	p < 0
	d	p ≠ 0.7

2. Which of the following statements about a confidence interval is NOT true?

a		A confidence interval of size α indicates that there is a probability of α that the parameter of interest falls inside the interval.
b		A confidence interval is generally constructed by taking a point estimate plus or minus the margin of error.
c		A confidence interval is often more informative than a point estimate because it accounts for sampling variability.
d		A confidence interval provides a range of plausible values for a parameter based on the sampling distribution of a point estimator.

3. Suppose that the sample proportion p̂ is used to construct a confidence interval for the population proportion p. Assuming that the value of p̂ is fixed, which of the following combinations of confidence levels and sample sizes yield the the widest confidence interval (that is, one with the largest range of values)?

a		99% confidence level, n = 500
b		95% confidence level, n = 500
c		99% confidence level, n = 50
d		95% confidence level, n = 50

4. Which of the following statements about hypothesis testing is true?

	a	If the data provide sufficient evidence for the null hypothesis, then the conclusion is to reject H1.
	b	A hypothesis test provides a plausible range of values for a parameter.
	c	If the data provide sufficient evidence for the alternative hypothesis, then the conclusion is to reject H0.
	d	A hypothesis test uses sample data to determine which of two competing hypotheses is true.

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

9. For a one-sided hypothesis test in which the test statistic is z_obs, which of the following critical values is appropriate if a 5% significance level is desired?

a		1.645
b		1.960
c		2.326
d		2.576

10. For a particular scenario, we wish to test the hypothesis H₀ : p = 0.52. For a sample of size 50, the sample proportion p̂ is 0.42. Compute the value of the test statistic z_obs. (Express your answer as a decimal rounded to two decimal places.)

Answer 1

dear student we can provide you with the solution of 4 sub question at a time.

1) option B and C is right

One-tailed hypothesis tests are also known as directional and one-sided tests because you can test for effects in only one direction.

p>0.3

p<0
is right

2) option A is not true

The X% confidence interval defines a range of values that you can be X% certain contains the population parameter it is not the probability.

3) margin of error for the population proportion confidence interval is

option C is right as will be maximum for 99% confidence and n is less for n = 50

Thus the confidence interval will be widest for C

4) option C is right