1) How many values can R, take? 2) Consider using the Wald test at asymptotic level a = 5% for this test. Assuming that the null hypothesis is true, what is the actual probability of type 1 error for this test?
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- A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1 2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Amount by Which Speed Limit Was Exceeded MaleDriver FemaleDriver 1.2 -0.1 1.4 0.4 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use μmales − μfemales.Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to…A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1 2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Amount by Which Speed Limit Was Exceeded MaleDriver FemaleDriver 1.3 -0.1 1.3 0.4 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use μmales − μfemales.Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to…given normally distributed sample x=12 and s=3, use the Empirical Rule determine the upper and lower bounds to contain approximately 95% of your data
- The test statistic of z=−2.85 is obtained when testing the claim that p=1/2. a. Using a significance level of α=0.05, find the critical value(s). b. Should we reject H0 or should we fail to reject H0?A researcher obtains t=2.25 for a repeated measures study using a sample of n=10 participants. Based on this t value, what is the correct decision for a two- tail test at .05 and .01 alpha level?A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…
- A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results. Heater Wattage Area 1 1,000 108 2 750 291 3 1,500 100 4 1,000 43 5 1,250 68 6 1,500 181 7 1,250 254 8 750 228 9 1,500 126 10 1,500 166 11 750 45 12 750 237 13 1,000 75 14 1,750 126 15 1,750 249 16 1,750 105 17 1,750 298 18 1,250 212 19 750 98 20 750 185 Click here for the Excel Data File a. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Round your answer to 4 decimal places.) b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.050 significance level. (Round intermediate calculations and final answer to 3 decimal places.)H0: ρ ≤ 0; H1: ρ > 0 Reject H0 if t > 1.734…In a test of H0: p = .43 versus Ha: p ≠ .43, a sample of size 1500 leads to a p-value of 0.087. Which of the following must be true if a = 0.05? A. The Ho should be rejected at the 5% level B. The Ho should fail to be rejected at the 5% level C. The Ho should be accepted at the 5% levelIf X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameter
- I am a little unclear on how to obtain the p value given the z value and how to determine the tail tests. Can you go a bit more in depth on that part?Let X1,...,Xn be an iid sample from f(x | θ) = θ xθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θLet X1, . . . , Xn be an iid sample from f(x | θ) = θxθ−1 , 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ.
