A large number of examples on Testing of Null hypothesis for largeand small samplesare given below:3.Let p be the probability that a coin will turn up heads and x bethe number of heads obtained in tossing the alternative hypothesis(a) H₁:p<0.5 at a = 0.05 with x = 45..(b)H₁: p0.5 at α = 0.05 with x = 38.H₁:p>0.5 at a = 0.05 with x = 67.(c)

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Answered: A large number of examples on Testing…

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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What is the critical value for an upper‐tailed hypothesis test of the population mean when the population variance is unknown in which a null hypothesis is tested at the 0.10 level of significance based on a sample size of 19? 1.645 1.328 1.734 1.740
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. H0: μ ≥ 220 H1: μ < 220 (a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.
Sample of 40 sizes were taken from Group A and a sample of 39 sizes were taken from Group B. Group A had a sample average of 3.5 and Group B had a sample average of 3.9. Group A standard deviation is 1.1 and standard deviation of Group B is 1.9. Test to see if there is a statistically significant difference between the average sizes using a 5% level of significance. Which is the most logical conclusion: 1) There is not enough evidence to support that the mean sizes are different or 2) We reject the null hypothesis that there is no difference between the mean sizes? Why?
A series of tests are performed to test a particular hypothesis. The significance level is fixed to be 0.05. The characteristics of the tests are as follows Test 1: Has a significance level of 0.5, power of the test is 0.92 Test 2: Has a significance level of 0.1, power of the test is 0.73 Test 3: Has a significance level of 0.01, power of the test is 0.65 Test 4: Has a significance level of 0.2, power of the test is 0.99 Test 5: Has a significance level of 0.025, power of the test is 0.33 The most powerful test among the above mentioned tests is/are ______.
We want to conduct a hypothesis test of the claim that the population mean number of holding penalties during a college football game is less than 2.4penalties per game. So, we choose a random sample of games. The sample has a mean of 2.5penalties per game and a standard deviation of 0.8 penalties per game. For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places. (a) The sample has size 100and it is from a non-normally distributed population with a known standard deviation of 0.69. O Z O T O It is unclear which test statistic to use. (b) The sample has size 18, and it is from a population with a distribution about which we know very little. O Z = O t = O It is unclear which test statistic to use
suppose the p value in a two tailed test is 0.0134 based on the same population sample and null hypothesis and assuming the test statistics z is negative what is the p value for a corresponding oat tailed test
The environmental research scientists report that the exhaust emissions for a certain car model has a normal distribution with a mean of 1.45 grams of nitrous oxide per mile and a standard deviation of 0.4. The car manufacturer claims their new process reduces the mean level of exhaust emitted for this car model. A Simple random sample of 36 cars is taken and the mean level of exhaust emitted for this sample is 1.21 grams. (a) State the null and alternative hypotheses. (b) Calculate the test statistic. (c) Calculate the Zc and p-value. Draw the picture. (d) What is the decision at the 0.05 significance level?
Question 4 Suppose we are testing the null hypothesis Ho: p=0.3, and want to use a significance level of a = 0.05. What sample size should we use if we want a power [probability to correctly reject Ho in the proper direction] of 75% when the true proportion is p = 0.35? Please round up and report your answer to the next highest whole number. Question 5 Suppose we are testing the null hypothesis Ho: p=0.4, and will gather data from N = 200 respondents. If we are using a 90% confidence interval, what is the power of our test to detect if the true proportion was p = 0.3? Please round your answer to 2 decimal places; do NOT convert to a percentage. Question 6 Suppose we are testing the null hypothesis Ho: p= 0.85, and will gather data from N= 318 respondents. If we are using a 95% confidence interval, what is the power of our test to detect if the true proportion was p = 0.82? Please round your answer to 2 decimal places; do NOT convert to a percentage.
If the variance in the weights of one sample of 12 oz. cookies is 3 oz. and the variance in a second sample, made in another factory, is only 1 oz. is there a real difference in variances between the two? (Estimate at 95% probability level, using 2-tail test). Use the appropriate test statistic to determine this, and assume there are 9 degrees of freedom for each sample. Yes no maybe none of the above.
You wish to test the claim that the average IQ score is less than 100 at the .10 significance level. You determine the hypotheses are: Ho: μ=100Ho: μ=100 H1:μ<100H1:μ<100 You take a simple random sample of 73 individuals and find the mean IQ score is 95.2, with a standard deviation of 15.1. 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…
The body weight of a healthy 3-month-old colt should be about ? = 74 kg. You want to set up a statistical test to challenge the claim that ? = 74 kg. Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than 74 kg. State the null hypothesis H0 and the alternate hypothesis H1 . H0 : ? H1 : ? What kind of test is this? right-tailed testtwo-tailed test left-tailed test
#22).

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