4 Let X be a rs of size n from N(0,1), 0 € {0,1}. Find an MP size-a test for the following hypotheses: Ho: 0 = 0 H: 0 = 1 Vs
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- Model Model Model ModelCurrent New Current New Current New Current New264 277 270 272 263 274 281 283261 269 287 259 264 266 274 250267 263 289 264 284 262 273 253272 266 280 280 263 271 263 260258 262 272 274 260 260 275 270283 251 275 281 283 281 267 263258 262 265 276 255 250 279 261266 289 260 269 272 263 274 255259 286 278 268 266 278 276 263270 264 275 262 268 264 262 279 1. Formulate and present the rationale for a hypothesis test that Par could use to comparethe driving distances of the current and new golf balls.2. Analyze the data to provide the hypothesis testing conclusion. What is the p-valuefor your test? What is your recommendation for Par, Inc.?3. Provide descriptive statistical summaries of the data for each model.4. What is the 95% confidence interval for the population mean driving distance ofeach model, and what is the 95% confidence interval for the difference between themeans of the two populations?5. Do you see a need for larger sample sizes and more testing with…Suppose that the finite population being studied has N elements from which a sample of size n is drawn using SRSWOR to estimate the population total LOOK AT THE IMAGE ATTACHEDSuppose that Y,.,Y, are independent and identically distributed continuous uniform random variables such that Y-u[0, e] for i e (1, .,n}, where e>0 is an unknown parameter. (a) Construct the most powerful test of size a of the hypotheses Họ: 0 = 0, against H;: 0 = 6, where 0, > 0, >0 and a e (0, 1).
- A survey was conducted of newlyweds in a country who have a spouse of a different race or ethnicity from their own. The survey included random samples of 1000 newlyweds in Ethnicity A and 1000 newlyweds in Ethnicity B. In the survey, 14% of respondents in Ethnicity A and 21% of respondents in Ethnicity B had a spouse of a different race or ethnicity from their own. At α = 0.01, is there evidence to support the claim that the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own is less than the proportion of newlyweds in Ethnicity B that have a spouse of a different race or ethnicity from their own? Let p₁ represent the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own. Let p2 represent the proportion of newlyweds in Ethnicity B that have a spouse of a different race or ethnicity from their own. State the null and alternative hypotheses. A. Ho: P₁ P2 B. Ho: P₁ P2 Ha: P₁ P2 OC. Ho:…4.11 For the ARMA(1,2) model Y₁ = 0.8Y₁ _ 1 + e + 0.7et − 1 + 0.6et – show that 2, (a) Pk = 0.8pk-1 for k>2. (b) p2 = 0.8p₁ +0.60²/10-A medical researcher says that less than 85% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that country, 83% think that healthy children should be required to be vaccinated. At α=0.01, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. Less than 8585% of adults in the country think that healthy children should be required to be vaccinated. Your answer is correct. B. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not enter your response here%. C. More than enter your response here% of adults in the country think that healthy children…
- X is an exponential random variable with parameter λ = 1/4 Calculate P {X ≤ 4}Consider the accompanying data on plant growth after the application of different types of growth hormone. 1: 12 18 7 15 2: 20 13 21 17 3: 19 16 21 17 4: 8 10 17 9. 5: 12 16 8 In USE SALT (a) Perform an F test at level a = 0.05. State the appropriate hypotheses. O Ho: H1# Mz # H3# H4#H5 : all five u,'s are equal O Ho: Hy # Mz # Hz# H4# H5 : at least two µ,'s are equal O Ho: H1 = H2 = H3 = H4= H5 H: at least two µ's are unequal Hoi H1 = Hz= Hz = H4= M5 : all five u,'s are unequal Calculate the test statistic. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? O P-value > 0.100 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 0.001 < P-value < 0.010 O P-value < 0.001Consider the simple regression model Yi = B1 + B2r; + €i, E; n iid N(0, o²) with pdf for observation i is given by: 1 exp 1 (yi – B1 – Bori)²] V2no? o2 a. Given the iid sample (y1, r1),..., (YN, rN), derive the maximum likelihood estimator of Bo and B1. b. Derive the variance of the maximum likelihood estimator of Bo and B1. c. Show that maximizing the log L(B,02|y, r) corresponds to minimizing SSR.
- Suppose we take a random sample of size 25 form Bi(10, p). Find the pmf and the CDF of the 5th order statistic Y3.Consider drawing samples of size n = 12 from U(0,12) Consider estimators for the population variance. One such estimator is the familiar s. When you draw such a sample, what is E(s') ? Another is the sample range r, where r= ymax - Ymin %3D When you draw such a sample, what is E(r) ? Hint: E(y max) = 144/13 using Theorem 3.10.1 Isr unbiased? Isr consistent?A medical researcher says that less than 85% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that country, 83% think that healthy children should be required to be vaccinated. At α=0.01, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. Less than enter your response here% of adults in the country think that healthy children should be required to be vaccinated. B. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not enter your response here%. C. More than enter your response here% of adults in the country think that healthy children…
