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Exam 9: One-Sample Hypothesis Tests

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Question 1

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Regarding the probability of Type I error (α) and Type II error (β) , which statement is true?

A) β > α
B) β < α
C) α + β = 1
D) Power = 1 - β.

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Question 2

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The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. The p-value for a right-tailed test is:

A) .1337
B) .4192
C) .0901
D) .0808

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Question 3

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We can assume that the sample proportion is normally distributed if:

The researcher's null hypotheses is H₀: σ² = 420. A sample of n = 18 items yields a sample variance of s² = 512. The test statistic is:

A hypothesis test may be statistically significant, yet have little practical importance.

In a two-tailed test, a statistician got a z test statistic of 1.47. What is the p-value?

A power curve for a mean is at its lowest point when the true μ is very near μ₀.

If sample size increases from 25 to 100 and the level of significance stays the same, then:

Given that in a one-tailed test you cannot reject H₀, can you reject H₀ in a two-tailed test at the same α?

If the null and alternative hypotheses are H₀: μ ≤ 100 and H₁: μ > 100, the test is right-tailed.

For a right-tailed test of a hypothesis for a population mean with n = 14, the value of the test statistic was t = 1.863. The p-value is:

In graphing power curves, there is a different power curve for each sample size n.

In the hypothesis H₀: π = π₀, the value of π₀ is derived from the sample.

Increasing the level of significance shifts the power curve upward, ceteris paribus.

For a right-tailed test of hypothesis for a population mean with known σ, the test statistic was z = 1.79. The p-value is:

Power is the probability of rejecting the null hypothesis when it is false and is equal to 1 - β.

Which of the following is correct?

"Currently, only 20 percent of arrested drug pushers are convicted," cried candidate Courageous Calvin in a campaign speech. "Elect me and you'll see a big increase in convictions." A year after his election a random sample of 144 case files of arrested drug pushers showed 36 convictions. For a right-tailed test, the p-value is approximately:

In hypothesis testing, we are trying to prove the null hypothesis.

The critical value of a hypothesis test is based on the researcher's selected level of significance.