Hypothesis Testing for the Population Mean 277.71 263.53 200.58 231.29 309.30 285.77 276.01 370.76 265.81 348.71 202.05 252.41 246.86 253.79 231.37 383.96 397.87 245.06 300.95 371.36 391.52 332.77 220.05 384.59 222.47 267.30 318.62 304.65 221.26 259.28 239.83 229.82 274.59 283.99 373.91 305.23 245.70 281.98 363.24 331.53 285.11 357.00 387.68 362.02 321.58 394.10 391.10 275.80 252.28 380.05 389.30 352.38 317.30 288.95 275.98 377.40 301.28 325.16 379.16 400.65 318.41 309.41 342.71 233.33 325.63 276.21 299.19 Suppose that you want to run a hypothesis test on the population mean. The data comes from a normally distributed population with a population standard deviation that is unknown. Set up a two-tailed hypothesis test to test whether the population mean is equal to 330. Use a level of significance of 0.05. Provide the following: a. State your null and alternative hypotheses. Use a two-tailed test. b. Determine the test statistic. c. Determine the p-value. d. Determine the critical values for the hypothesis test. e. Clearly explain whether one should reject or not reject the null hypothesis at a 5% level of significance. Explain your reasoning.
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Step 1
State your null and alternative hypotheses. Use a two-tailed test. The null hypothesis (H0) is that the population mean is equal to 330, and the alternative hypothesis (H1) is that the population mean is not equal to 330. H0: μ = 330 H1: μ ≠ 330 b. Determine Show more…
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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.
Robin C.
In order to conduct a hypothesis test for the population mean, a random sample of 13 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 16.0 and 1.9, respectively. Use Table 2. Use the p-value approach to conduct the following tests at α = 0.10. H0: μ ≤ 15.4 against HA: μ > 15.4 a-1. Calculate the value of the test statistic. (Round your answer to 2 decimal places.) Test statistic b. Approximate the p-value. 0.050 < p-value < 0.100 0.010 < p-value < 0.020 0.100 < p-value < 0.200 c. What is the conclusion? Do not reject H0 since the p-value is greater than α. Do not reject H0 since the p-value is less than α. Reject H0 since the p-value is greater than α. Reject H0 since the p-value is less than α.
Adi S.
Perform a hypothesis test for the mean for the following sample, the significance level alpha is 5%. Sample: 3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 3.3, 5.5, 3.7, 2.8, 4.4, 4, 5.2, 3, 4.8. Population standard deviation is =1.05. Test if mean is greater than 3.16. Assume normality of the data. 1 Formulate the hypothesis by entering the corresponding signs: "<", ">", "=" or "≠" and numbers. Hint: in your answers use "<>" instead of "≠". H0: mean H1:mean 2 Test statistics value (rounded to two decimal places): 3 Conclusions, based on the results, which of the following options is correct: (type the corresponding capital letter, do not type the "dot" at the end) A. Reject H0 and accept H1 at 5% significance level. B. Accept H0 with 95% confidence. C. Do not reject H0 at 5% significance level and reserve judgement. D. Reject both, H0 and H1, the test has failed. E. Accept both, H0 and H1, the test has failed.
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