4) In the following null and alternative hypotheses Họ : u =68 and HA: H+ 68 , a = 0.02 , x = 69.02 , o = 5.4 and n= 40 a. State the decision rule in terms of the critical value of the test statistic. b. State the calculated value of the test statistic. c. State the conclusion. d. Compute the p - value. Does its value support the claimed obtained in part a justify.
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- The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…Assume we wanted to show that the true proportion of virginica iris seeds that fail to germinate is less than 20%. Let's say we tested at an alpha of 0.05, and found a p-vale of 0.082. Which of the following would be an appropriate conclusion and interpretation? A) With an alpha of 0.05, and a p-value of 0.082, we fail to reject the null and state we have insufficient evidence to support that the true proportion of virginica iris seeds that fail to germinate is less than 20%. B) With an alpha of 0.05, and a p-value of 0.0082, we reject the null and state we have sufficient evidence to support that the true proportion of virginica iris seeds that fail to germinate is less than 20%. C) With an alpha of 0.05, and a p-value of 0.082, we reject the null and state we have sufficient evidence to support that the true proportion of virginica iris seeds that fail to germinate is less than 20%. D) With an alpha of 0.05, and a p-value of 0.082, we fail to reject the null and state…A researcher who wants to know whether the proportion of male births in a hospital is different from the established baseline of 51.07%, would like to test the following hypotheses: Ho:P = 0.51 vs. Ha :P = does not equal 0.51 a) Is the alternative hypothesis upper tail, lower tail, or two tailed? b) What do you conclude if the test results p-value of 0.03 at alpha value = 5% c) What do you conclude if the test results p-value of 0.08 at alpha value = 10%
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- 2. Consider a study where students are measured on whether they had an internship during their time at WKU (Y/N) and whether they had a job at graduation (Y/N). If we wanted to test whether having an internship was associated with having a job at graduation (i.e., internship holders were more likely to have jobs), why would the chi-square test be inappropriate for this hypothesis? How should we analyze our data?Assume we wanted to show that the true average height of students is less than 63 inches. Let's say we tested at an alpha of 0.05, and found a p-value of 0.0315. Which would be an appropriate conclusion and interpretation? A) With an alpha of 0.05, and a p-value of 0.0315, we reject the null and state we have sufficient evidence to support that the true average height of students is less than 63 inches. B) With an alpha of 0.5, and a p-value of 0.0315, we reject the null and state we have sufficient evidence to support that the true average height of students is less than 63 inches. C) With an alpha of 0.05, and a p-value of 0.0315, we fail to reject the null and state we have insufficient evidence to support that the true average height of students is less than 63 inches. D) With an alpha of 0.05, and a p-value of 0.0315, we fail to reject the null and state we have sufficient evidence to support that the true average height of students is greater than or equal to…A test of H0H0:μ=1:μ=1 against HaHa:μ>1:μ>1 has test statistic zz = 1.74. Answer "Yes/Y" or "No/N" to the following questions. Is this test significant at the 2.5% level (αα = 0.025)? Is it significant at the 0.5% level (αα = 0.005)?
- We tested to see if people who consumed caffeine had a lower average reaction time than those who didn’t consume caffeine at the alpha = 0.08 level. Assume we found a p-value of 0.5437. Which below would be an appropriate conclusion and interpretation? With an alpha of 0.08, and a p-value of 0.5437, we fail to reject the null and state we have insufficient evidence to support that the true average reaction time of caffeine consumers was less than that of non-caffeine consumers. With an alpha of 0.08, and a p-value of 0.5437, we reject the null and state we have sufficient evidence to support that the true average reaction time of caffeine consumers was less than that of non-caffeine consumers. With an alpha of 0.08, and a p-value of 0.5437, we fail to reject the null and state we have sufficient evidence to support that the true average reaction time of caffeine consumers was less than that of non-caffeine consumers. With an alpha of 0.08, and a p-value of 0.5437, we…Consider the following: In general, when people diet they typically lose 10 lbs. (?σ = 2). A random sample of 16 people on the keto diet lost 15 lbs. Do people on the keto diet lose more or less weight than people on diets in general? 3. What is the Null Hypothesis? a)On average, weight loss in the keto diet sample does not differ from weight loss in the population of dieters in general. (H0: X-bar = Mu)) b)On average, weight loss in the keto diet sample does not differ from weight loss in the population of dieters in general. (H0: X-bar does not equal Mu) c)On average, weight loss in the keto diet sample differs from weight loss in the population of dieters in general. (H0: X-bar does not equal Mu) d)On average, weight loss in the keto diet sample differs from weight loss in the population of dieters in general. (H0: X-bar = Mu)Consider the following two formulations of the bivariate PRF, where ui and εi are both mean-0 stochastic disturbances (i.e random errors): yi = β0 + β1xi + u yi = α0 + α1(xi − x¯) + ϵ a) Write the OLS estimators of β1 and α1. Are the two estimators the same? b) What is the advantage, if any, of the second model over the first?