Suppose we are testing the null hypothesis Ho: mu = 20 and the alternative Ha: mu does not equal 20, for a normal population with sigma = 5. A random sample of 25 observations are drawn from the population, and we find the sample mean of these observations is X bar = 17.6. The P-value is closest to (A) 0.0164 (B) 0.0668 (C) 0.1336 (D) 0.0082
Since , the population standard deviation is known.
Therefore , use normal distribution
Since , the test is two-tailed test.
The test statistic is ,
The p-value is ,
p-value=
; From standard normal distribution table
Suppose we are testing the null hypothesis Ho: mu = 20 and the alternative Ha: mu...
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 ____.
9 Test the null hypothesis Ho : u = 3.0against the alternative hypothesis HA: U < 3.0 , based on a random sample of 25 observations drawn from a normally distributed population with ū = 2.8 and o = 0.70. a) What is the value of the test statistic? Round your response to at least 3 decimal places. Number b) What is the appropriate p-value? Round your response to at least 3 decimal places. Number c) Is the null hypothesis...
Intro to Statistics: Q1: Q2: Q3: [8-1] Suppose we are testing the null hypothesis Ho: u = 50 and the alternative Ha: u 50 for a normal population with o 6. We took an SRS sample of size 48 and obtained x-bar 53. The P-value for the test is: 0.05 <0.05 Question 2 (0.5 points) 8-2] When performing a one-sample t-test, if the sample size is 14, then of freedom should be used for determining the confidence interval from the...
Suppose that we are testing the null hypothesis that μ = 68 versus the alternative that μ < 68. We take a sample of size 36 and find a sample average of = 63.4 and a sample standard deviation of s = 12.6. Determine the value of the test statistic for the hypothesis test of one population mean. t = -2.19 t = -0.37 t = 0.37 t = 2.19
4. Find the critical region of the likelihood ratio test for testing the null hypothesis Ho o aainst Ho on the basis of a random sample of sizen from a Follow the steps below normal population with the unknown mean for be the parameter space for(,o), and o be the subs et of 4-1) Let hypothesis , The parameter space can be expressed as Q= {-0< uo,0>0 Express similarly. (1 point) [Hint] 2 under the null hypothes is. Express the...
7. For any hypothesis test: b) Write down the appropriate alternative hypotheses and give the formula for the each test statistic, if any, for the following null hypothesis testing population normally distributed population not normal population not normal population not normal population normal population normal population not normal () Ho: So n 80, s 29 (iii) Ho: μ-Ha n-15, σ-25 (iv) Ho: μ=Ha n= 15, s = 36 (v) Ho: μ>Ha n= 10, σ = 16 (vi) H0'μ Han-60, σ-81...
In a hypothesis testing problem a researcher wants to test the hypothesis Ho 20 versus Ha 20 A sample of size 100 yielded a sample mean x = 19.25 and a sample standard deviation s 2.5. The P-value for the above test is 0013 .5000 0026 0147 0294
State the null hypothesis Ho and the alternative hypothesis Ha that would be used for a hypothesis test related to each of the following statements. The average GPA of students enrolled in an AP Statistics class is higher than 3.5. (2 points) The average retirement age of professional bull riders is less than 30 years. (2 points) The mean life of incandescent bulbs is at least 750 hrs. (2 points) The mean weight of college football players is no more...
Question 37 1 pts In null hypothesis testing, the null hypothesis (Ho) states that: There is a relationship in the population and that the relationship in the sample reflects the relationship in the population There is no relationship in the population and that the relationship in the sample reflects only sampling error If there is a relationship in the population there will be a relationship in the sample too If there is no relationship in the population there will be...
For each of the hypothesis testing problems, find the followin a) State the null and alternative hypotheses. b) Calculate the expected results for the hypothesis test a. suming the null hypothesis is true and determine the hy pothesis test model, c) Formulate the decision rule. d) Determine the statistical result and test statistic. e) Determine the conclusion and answer the question(s) posed in the problem, if any The population norms (ie, parametersu, andơ) for a math- ematics anxiety test are...