Why is the null hypothesis H0: μ = 0?
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Why is the null hypothesis H0: μ = 0?
Hypotheses:
Hypotheses is the plural form for hypothesis. Hypothesis is a statement about the population parameter like mean, proportion and standard deviation. Moreover, the hypothesis represents the assumption about the probability distribution of one or more variables.
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- 3. A researcher is testing a two-tailed null hypothesis at the p < .01 level with df = 45. What critical value would she or he use? Justify your answerImagine that your null hypothesis is σ2 = 10 and your alternative hypothesis is σ2 > 10. What is the critical value for the test statistic given α = 0.05 and n = 12?Suppose Y1,...,YN are independent random variables, each with the Pareto distribution and E(Yi) = (ß0 + ß1xi)2 Is this a generalized linear model? Give reasons for your answer. This is what I know: I know that the Pareto distribution is part of the exponential family. So, it meets the first criteria for a generalized linear model. However, I cannot figure out if this question is canonical, natural, or neither. For example, I know some exponential families are not in the exponential dispersion family used in generalized linear models unless a scale parameter is added and interpreted as a dispersion parameter. This is what I need help with: Please explain if this question is canonical, natural, or neither and to recognize the difference.Thanks!
- A doctor recorded the number of miles walked each day by patients over age 60 and the number of doctor visits in a year for 40 patients. The resulting data were used to conduct a hypothesis test to determine whether there is a linear relationship between the number of miles walked and the number of doctor visits. What are the correct hypotheses for the test?You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table. Category ObservedFrequency ExpectedFrequency A 12 B 15 C 6 D 10 E 13 Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places, and remember to use the unrounded Pearson residuals in your calculations.)χ2=χ2= What are the degrees of freedom for this test?d.f.= What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null accept the alternative As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that all 5…Suppose we want to test the null hypothesis Ho: p = 0.28 against the alternative hypothesis H1 :p + 0.28. Suppose also that we observed 100 successes in a random sample of 400 subjects and the level of significance is 0.05. What is the observed test statistic for this test? Select one: а. -1.521 O b. 1.336 С. -1.336 d. 1.521
- 11. In a recent poll, 16% of political Independents approve of Congress (N = 200). Among registered Republicans (N = 150), 10% approve of Congress. Test the null hypothesis that Congressional approval is the same between Republicans and Independents (alpha = 0.1).A laboratory claims that the mean sodium level, µ, of a healthy adult is 140 mEq per liter of blood. To test this claim, a random sample of 20 adult patients is evaluated. The mean sodium level for the sample is 137 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 15 mEq. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the population mean adult sodium level differs from that claimed by the laboratory? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)1. A Random Variable X can take only two values, 1 and 2 .P(1) = 0.8 and P(2) = 0.2 Calculate the Expected value of X. 2. A Random Variable X can take only two values, 1 and 2. P(1) = 0.8 and P(2) = 0.2 Calculate the Variance of X 3. A lottery that pays off 100,000 pesos is made available for 5,000,000 tickets. Each ticket costs 50 pesos. Suppose the variable X gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only one ticket? 4. In a deck of cards which consists of cards numbered 1 to 5, a card is drawn randomly. A player wins 35 pesos if the number on the card is odd and loses 35 pesos if the number on the card is even. What is the expected value of his winnings?
- Which of the answers below is the most likely explanation for the following discrepancy. Suppose we have a comparison of 3 means. The sample sizes are nį = 3, n2 = 3, n3 = 4. We use Monte Carlo simulation to calculate the p-value for the null hypothesis Ho : F1(x) = F2(x) = F3(x). We do 1000 simulations and find 15 simulations result in an F-statistic as large as or larger than the observed value. The p-value based on the exact permutation distribution was found to be p=0.010. Since this p-value would suggest a non- significant test at a = 0.010 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Our Monte Carlo program must be wrong because the simulated p-value always equals the exact p-value. b We should not expect the simulated p-value p-value to equal the exact p-value. We should have continued running simulations until the simulated p-value equals the exact p-value. d We know that the simulated p-value is always larger than the…Suppose there is a claim that a certain population has a mean, µ, that is less than 7. You want to test this claim. To do so, ybu collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis, H, and the alternative hypothesis, H,, as follows. Ho: H=7 H: µ<7 Suppose you also know the following information. The value of the test statistic based on the sample is -1.995 (rounded to 3 decimal places). The p-value is 0.023 (rounded to 3 decimal places). (a) Complete the steps below for this hypothesis test. Standard Normal Distribution 0.4 Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed 0.3- Step 2: Enter the test statistic. (Round to 3 decimal places.) SubrWhat are the hypotheses for the t-test? Let population 1 be weights before therapy and let population 2 be weights after therapy. A. H0: μ1=μ2 Ha: μ1<μ2 B. H0: μ1=μ2 Ha: μ1≠μ2 C. H0: μ1>μ2 Ha: μ1<μ2 D. H0: μ1=μ2 Ha: μ1>μ2 Part 2 Find the test statistic. t= (Round to two decimal places as needed.) Part 3 Find the P-value. The P-value is (Round to three decimal places as needed.) Part 4 What is the conclusion for the hypothesis test? ▼ Do not reject Reject H0; the data ▼ provide do not provide sufficient evidence at the 1% significance level that the mean weight ▼ after therapy is greater. before and after therapy differ. before therapy is greater.
