Suppose there is a claim that a certain population has a mean, ( mu ), that is different than 9. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.10 level of significance. To start this test, you write the null hypothesis, ( H_{0} ), and the alternative hypothesis, ( H_{1} ), as follows. [ egin{array}{l} H_{0}: mu=9 \ H_{1}: mu eq 9 end{array} ] Suppose you also knew the following information. The value of the test statistic based on the sample is 1.896 (rounded to 3 decimal places). The p-value is 0.058 (rounded to 3 decimal places). (a) Complete the steps below for this hypothesis test. (b) Based on your answer to part (a), which statement below is true? Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. Since the p-value is greater than the level of significance, the null hypothesis is rejected. Since the p-value is greater than the level of significance, the null hypothesis is not rejected.
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In this case, the hypotheses are already stated as: \[ H_{0}: \mu = 9 \] \[ H_{1}: \mu \neq 9 \] This setup indicates a two-tailed test because the alternative hypothesis suggests the population mean could be either less than or greater than 9. Show more…
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Suppose there is a claim that a certain population has a mean, that is equal to. You want to test this claim. To do so, you 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 Ho and the alternative hypothesis H, as follows: Ho: μ = 5 H1: μ ≠ 5 Suppose you also know the following information. The critical values are ±1.960 (rounded to 3 decimal places). The value of the test statistic is 2.574 (rounded to 3 decimal places). Complete the steps below to show the rejection region(s) and the value of the test statistic for this test. Normal Distribution Step 1: Select one-tailed (o-tailed): One-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places) Step 3: Enter the test statistic (Round to 3 decimal places) Based on your answer to part (a), choose the correct statement. The value of the test statistic lies in the rejection region. The value of the test statistic doesn't lie in the rejection region. Based on your answer to part (b), which statement below is true at the 0.05 level of significance? The null hypothesis should be rejected. The null hypothesis should not be rejected.
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The P-value for a hypothesis test is shown: Use the P-value to decide whether to reject Ho when the level of significance P=0.0507. (a) Do you reject or fail to reject Ho at the 0.01 level of significance? Reject Ho because the P-value, 0.0507, is less than α = 0.01. Do you reject or fail to reject Ho at the 0.05 level of significance? Fail to reject Ho because the P-value, 0.0507, is greater than α = 0.05. Do you reject or fail to reject Ho at the 0.10 level of significance? Fail to reject Ho because the P-value, 0.0507, is greater than α = 0.10.
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Hypothesis Test for a Population Mean (σ is Known) You wish to test the following claim (Ha) at a significance level of α=0.10: Ho: μ = 69.9 Ha: μ < 69.9 You believe the population is normally distributed and you know the population standard deviation is σ = 13.5. You obtain a sample mean of M = 61 for a sample of size n = 25. 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 three decimal places.) P-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null hypothesis accept the null hypothesis fail to reject the null hypothesis As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 69.9. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 69.9. The sample data support the claim that the population mean is less than 69.9. There is not sufficient sample evidence to support the claim that the population mean is less than 69.9.
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