HomeworkLib
Question

Suppose you want to test H0 : µ = 4 against Ha : µ > 4....

Suppose you want to test H0 : µ = 4 against Ha : µ > 4. In addition, suppose that σ = 5, n = 36, and you
will reject H0 if x > 5 and accept H0 otherwise. (a) (6 pts) Find the power of this test against the alternative µ = 5.6. (b)
(2 pts) Find the probability of a Type II error in this situation (just use your answer from part (a) to help you do this).

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

a)

The power of the test is defined as,

Where, is the probability of type II error.

The probability is obtained by calculating the z score for mean,

Now, the probability is obtained from standard normal distribution table for z = 1.92 (In excel use function =NORM.S.DIST(1.92,TRUE))

b)

The probability of type II error is,

0 0
Add a comment
Know the answer?
Add Answer to:
Suppose you want to test H0 : µ = 4 against Ha : µ > 4....
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • We run a hypothesis test with H0 : µ = 40 against H1 : µ >...

    We run a hypothesis test with H0 : µ = 40 against H1 : µ > 40 at the 5% level of significance and find a test statistic of -1.88. If we used a sample of 22 with the population standard deviation, then give the critical value and decide if you accept or reject H0.

  • 2. If the test statistic for testing H0: µ≤ 10 vs. HA: µ > 10 at...

    2. If the test statistic for testing H0: µ≤ 10 vs. HA: µ > 10 at the .05 level is 1.641 and the sample size is 20, which of the following is true concerning the correct decision for the test, assuming that σ is unknown? A Type I error is possible A Type II error is possible Either a type I or II error is possible No error is possible 3. p-value for the test statistic

  • You read that a statistical test at the α=0.01 level has probability 0.14 of making a...

    You read that a statistical test at the α=0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative? Suppose we tested the null hypothesis that the weight of a McDonald's quarter pounder is 0.25 pounds (H0 : µ = 0.25) against the alternative that the weight is below 0.25 pounds (Ha : µ < 0.25). After collecting a sample our observed z statistic...

  • You read that a statistical test at the α=0.01 level has probability 0.14 of making a...

    You read that a statistical test at the α=0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative? Suppose we tested the null hypothesis that the weight of a McDonald's quarter pounder is 0.25 pounds (H0 : µ = 0.25) against the alternative that the weight is below 0.25 pounds (Ha : µ < 0.25). After collecting a sample our observed z statistic...

  • Suppose the null hypothesis is Ho : µ = 500 against Ha : > µ =...

    Suppose the null hypothesis is Ho : µ = 500 against Ha : > µ = 500 , and the significance level for this testing is 0.05. The population in question is normally distributed with standard deviation 100. A random sample of size n=25 will be used. If the true alternative mean is 550, then the probability of committing the type II error is ____.

  • In a test of H0: µ=150 against HA: µ<150, a sample of size 250 produces Z...

    In a test of H0: µ=150 against HA: µ<150, a sample of size 250 produces Z = -0.65 for the value of the test statistic. Thus the p-value is approximately equal to:

  • In a single sample t-test with H0: µ = 25 against HA: µ  25, a...

    In a single sample t-test with H0: µ = 25 against HA: µ  25, a sample of size 10 produced a sample mean of 26 and a computed t-value of 2.182. At the 0.05 level of significance, this means: A. there is sufficient evidence to conclude that µ not equal to 25 B. there is sufficient evidence to conclude that µ = 25 C. there is sufficient evidence to conclude that µ = 26 D. there is sufficient evidence...

  • Suppose you want to test the following hypotheses: H0: p ≥ 0.4 vs. H1: p <...

    Suppose you want to test the following hypotheses: H0: p ≥ 0.4 vs. H1: p < 0.4. A random sample of 1000 observations was taken from the population. Answer the following questions and show your Excel calculation for each question clearly: (a) Let p ̂ be the sample proportion. What is the standard error of sample proportion (i.e., σ_p ̂ ) if H0 is true? (b) If the sample proportion obtained were 0.38 (i.e., p ̂=0.38), what is its p-value?...

  • The five parts are: i. Null Hypothesis: H0 : µ =5.2 ii. Alternative Hypothesis: HA :...

    The five parts are: i. Null Hypothesis: H0 : µ =5.2 ii. Alternative Hypothesis: HA : µ < 5.2 iii. Rejection Region: Reject H0 if t statistic <−t49,.05 =−1.677 iv. Test Statistics: t = Y−µ0 S/pn = 5−5.2 0.7/p50 =−2.0203 <−t49,.05 =−1.677 v. Conclusion. Reject H0 at α = 5%. The data support that the mean dissolved oxygen count of the water is less than the reading at this location over the past year. What is the p-value?

  • 4. It is desired to test H0 : µ = 20 Vs H1 : µ <...

    4. It is desired to test H0 : µ = 20 Vs H1 : µ < 20, on the basis of a random sample of size 64 from normal distribution with population standard deviation σ = 2.4. The sample mean and sample standard deviation are found to be 19.5 and 2.5, respectively. (a) Test the hypothesis at α = 0.05. Compute the test statistics, critial regions, and perform the test. Will the result be difference if α is changed to...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT