Question

Suppose you are planning to use a test of the population mean when the population standard...

Suppose you are planning to use a test of the population mean when the population standard deviation is known (a z test) to test the following one-tailed hypotheses.

H₀: μ ≤ 0
H₁: μ > 0

Since you want to maximize the power of your study, you are considering which factors might decrease power so that you can adjust your plans to avoid them, if possible, before conducting your research.

The following are your considerations for decreasing power. Fill in any missing words/values. (Hint: Remember that for this alternative hypothesis, you will reject the null hypothesis for large values of the test statistic.)

  decreases the power of the z test, because this change in α makes it less likely you will reject the null hypothesis. This change makes it harder to correctly reject a false null hypothesis—meaning that power is decreased.
  in M decreases the power of the z test, because this change in the   of the test statistic for the z test   the overall test statistic, making it   likely you will reject the null hypothesis.
The denominator of the test statistic for the z test is   .   in this denominator decreases the power of the z test, because this change   the overall test statistic, making it less likely you will reject the null hypothesis. This denominator increases when either the sample size (n)   or the population standard deviation   .

All of the factors discussed previously affect the power of the z test. As the person making the decisions about how the research will be conducted, which of the following factors can you possibly influence? Check all that apply.

α

M

Sample size (n)

σ/√n

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Test the claim about the population mean μ at the level of significance α. Assume the...
Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed. Write out null and alternative hypotheses, your critical z-score and your z-test statistic. Decide whether you would reject or fail to reject your null hypothesis. Claim: μ > 28; α = 0.05, σ = 1.2 Sample statistics: x̅ = 28.3, n = 50 H0: Ha: Critical z-score: Z test statistic: Decision:
Test the claim about the population mean μ at the level of significance α. Assume the...
Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed. Write out null and alternative hypotheses, your critical t-score and your t-test statistic. Decide whether you would reject or fail to reject your null hypothesis. Claim μ ≥ 13.9 α = 0.05 Sample statistics: x̅ = 13, s = 1.3, n = 10 H0: Ha: t0: t-test statistic: Decision:
1. Test the hypothesis: Population appears to be normally distributed. Given the sample statistics n =...
1. Test the hypothesis: Population appears to be normally distributed. Given the sample statistics n = 20,  = 8.2, and s = 1.2, find the critical value(s) tcr and test statistic t for testing the claim μ = 8.6 at significance α = 10%. Then, state the conclusion of this hypothesis test. Select one: tcr = 1.729, t ≈ 1.491, fail to reject H0 tcr = 1.328, t ≈ 1.491, reject H0 tcr = −1.328, t ≈ −1.491, reject H0 tcr...
Questions D-F d) You conduct a hypothesis test for the population proportion. After you calculate the...
Questions D-F d) You conduct a hypothesis test for the population proportion. After you calculate the z test statistic, you find that your p-value = 0.059. Using alpha (α) = 0.05 level of significance, what is your decision regarding the null hypothesis? Choose from the following. - Reject the null hypothesis and reject the alternative hypothesis - Accept the null hypothesis - Do not reject the null hypothesis - Reject the null hypothesis and accept the alternative hypothesis e) You...
Use a​ t-test to test the claim about the population mean μ at the given level...
Use a​ t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. ​Claim: μ ≠ 24​; α=0.10    Sample​ statistics: x overbar = 21.4​, s = 4.2 ​, n equals = 11 What are the null and alternative​ hypotheses? Choose the correct answer below. A.H0​: μ≠24    Ha​: μ=24 B.H0​: μ≤24    Ha​: μ>24 C.H0​: μ=24 Ha​: μ≠24 D.H0​: μ≥24 Ha​: μ than<24...
True or False: Suppose we use a t-test for one population mean to test H0: μ...
True or False: Suppose we use a t-test for one population mean to test H0: μ = 3418 g and we reject H0 at α =.05, two-tailed. When we state that the hypothesis test result is "statistically significant at the 5% level", we mean that (mark each statement as true or false): A) There is a 5% (long-term) chance that the decision to reject Ho is incorrect B) There is strong evidence against the null hypothesis C) The study did...
A random sample of 100observations from a population with standard deviation 23.99 yielded a sample mean...
A random sample of 100observations from a population with standard deviation 23.99 yielded a sample mean of 94.1 1. Given that the null hypothesis is μ=90μ=90 and the alternative hypothesis is μ>90μ>90 using α=.05α=.05, find the following: (a) Test statistic == (b) P - value: (c) The conclusion for this test is: A. There is insufficient evidence to reject the null hypothesis B. Reject the null hypothesis C. None of the above 2. Given that the null hypothesis is μ=90μ=90...
You wish to test the following claim ( H a H a ) at a significance...
You wish to test the following claim ( H a H a ) at a significance level of α = 0.005 α = 0.005 . H o : μ = 53.3 H o : μ = 53.3 H a : μ ≠ 53.3 H a : μ ≠ 53.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 33 n = 33 with a mean of...
A sample​ mean, sample​ size, and population standard deviation are provided below. Use the​ one-mean z-test...
A sample​ mean, sample​ size, and population standard deviation are provided below. Use the​ one-mean z-test to perform the required hypothesis test at the 1​% significance level. x bar =26, n=36, σ=88​, H0​: mu=3, μ=31​, Ha​: mu < 31 Find test statistic Z?
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : μ = 59.6 H a : μ ≠ 59.6 You believe the population is normally distributed and you know the population standard deviation is σ = 8.7 . You obtain a sample mean of ¯ x = 64.2 for a sample of size n = 21 . What is the test statistic for this sample? test statistic...