Suppose we are testing the null hypothesis H0: μ = 16 against the alternative Ha: μ> 16 from a normal populationwith known standard deviation o=3. A sample of size 324 is taken. We use the usual z statistic as our test statistic.Using the sample, a z value of 2.21 is calculated. (Remember z has a standard normall distribution.)a) What is the p value for this test?b) Would the null value have been rejected if this was a 2% level test?ΟΝΟΥc) Would the null value have been rejected if this was a 1% level test?ΟΝΟΥd) What was the value of x calculated from our sample?

given data,hypothesis:H0:μ=16H1:μ>16σ=3n=324z=2.21

Answered: Suppose we are testing the null…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Using a random sample of n = 50, the sample mean is x ̅ = 297.6. Suppose that the population standard deviation is σ=12. Is the above statistical evidence sufficient to make the following claim: μ>295 right tail, one tail at the 1% level of significance? Write the null hypothesis Ho and alternative hypothesis Ha. Calculate the standard error. Calculate the z score. Calculate the p value. What is the conclusion?
You wish to test the claim that the average IQ score is less than 100 at the .01 significance level. You determine the hypotheses are: Ho: μ=100 H1:μ<100H You take a simple random sample of 79 individuals and find the mean IQ score is 98.3, with a standard deviation of 15.3. Let's consider testing this hypothesis two ways: once with assuming the population standard deviation is not known and once with assuming that it is known. Round to three decimal places where appropriate. Assume Population Standard Deviation is NOT known Assume Population Standard Deviation is 15 Test Statistic: t = Test Statistic: z = Critical Value: t = Critical Value: z = p-value: p-value: Conclusion About the Null: Reject the null hypothesis Fail to reject the null hypothesis Conclusion About the Null: Reject the null hypothesis Fail to reject the null hypothesis Conclusion About the Claim: There is sufficient evidence to support the claim that the average IQ score is less…
Consider a random sample of size n from a normal distribution with unknown mean u and unknown variance o?. Suppose the sample mean is X and the sample variance is S?. n = 16, the observed sample mean i is 8.9. the observed sample variance s? is 25 and 4o : 10.5. Suppose we now want to test Ho : o? = of versus H1 : o? + of. Which of these test statistics should we use? Select one: (n-1)s? W = of a. O b. Z %3D O c. T= S/n Let o = 36. What is the (appropriate) observed test statistic? Give answer to three decimal places. What is the p-value of the (appropriate) observed test statistic for testing Ho : o? = of versus H1 : o? + of you just computed? Give answer to three decimal places.
1. Find the variance of the t - distribution with 35 degrees of freedom. 2. Find the value of ta for a 95% confidence interval when the sample size is 25. 2 3. Find an interval of values for Z using the standard normal distribution, corresponding to an area of 91.3%
Q1: A researcher was interested in the effect of exercise on stress levels. For the general population, the distribution of the Stress Battery Scale scores is normal with the mean of µ = 25 and the standard deviation of σ = 5. A sample of n = 100 participants was asked to exercise for three weeks and then reported their stress levels. The sample mean was ?X = 23. Conduct a hypothesis test and determine the effect of exercise. Use the two-tailed test α = .01 1.Type the null and research hypotheses in complete sentences. 2.Cut off points 3.Standard error and z-score -show your computation process 4.Your conclusion thoroughly.
Consider a random sample of size n from a normal distribution with unknown mean u and unknown variance o?. Suppose the sample mean is X and the sample variance is S?. n = 16, the observed sample mean i is 8.9. the observed sample variance s is 25 and µo = 10.5. Suppose we now want to test Ho : o² = of versus H1 : o? + of. Which of these test statistics should we use? Select one: O a. W = (n-1)s O b. Z X-P O c. T = S/n Let of = 36. What is the (appropriate) observed test statistic? Give answer to three decimal places.
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This test statistic leads to a decision to... A.) reject the null B.) accept the null C.) fail to reject the null You wish to test the following claim (Ha) at a significance level of α=0.002α=0.002. Ho:μ=55.6 Ha:μ>55.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=601n=601 with mean ¯x=57.1x¯=57.1 and a standard deviation of s=19.9s=19.9.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = ___________What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = ____________The p-value is... A.) less than (or equal to) αα B.) greater than α As such, the final conclusion is that... A.) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 55.6. B.) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than…
What is the critical value? A. 2.33 B. 2.492 C. 2.575 D. 2.797
Suppose x has a normal distribution with σ = 9. A random sample of size 36 has sample mean 20. Find a 95% confidence interval for μ.
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. Determine the critical region using a one-tailed test with alpha = .05. Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). Based on your analysis, is there a relationship between the drug and attention span?
ATTEMPT ONLY IF YOU ARE 100% SURE

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