(1) A random sample of size n from an exponential population is used to test the null hypothesis o against the alternative H₁ : 0 = 0₁ > 00. Use the Neyman-Pearson lemma to find the most powerful critical region of size a, and indicate how to calculate the constant. =
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- The average drying time of a manufacturer’s paint is 20 minutes. Investigating the effectiveness of a modifica-tion in the chemical composition of her paint, the manu-facturer wants to test the null hypothesis μ = 20 minutes against a suitable alternative, where μ is the average dry-ing time of the modified paint. (a) What alternative hypothesis should the manufactureruse if she does not want to make the modification in thechemical composition of the paint unless it decreases thedrying time?(b) What alternative hypothesis should the manufactureruse if the new process is actually cheaper and she wants tomake the modification unless it increases the drying timeof the paint?Can attack of a plant by one organism induce resistance to subsequent attack by a different organism? In a study of this question, individually potted cotton plants were randomly allocated to two groups. Each plant in one group received an infestation of spider mites; the other group were kept as controls. After 2 weeks the mites were removed, and all plants were inoculated with a fungus that causes wilt disease. According to the research question, H0: Miles do not induce resistance to wilt. Ha: Mites do induce resistance to wilt. What is the alternative hypothesis in symbols when p represents the proportion of wilt disease in a group? p1 < p2 or p1 > p2?(11) Find the moment-generating function (MGF) of an exponential random variable with param- eter A.
- Consider the model defined by, wage; = Bo + B1 educ; + B2 age; + B3 tenure; + uj for 15 years of monthly data. The R2 calculated is 0.577, so compute the F statistic to test the null hypothesis H0: B1 = B2 = B3 = 0. The F statistic is? [2 decimal places required](d) Use a t-test to test if the relationship between years of experience and income is statistically significant at the 0.05 level of significance. State the null and alternative hypotheses. O Ho: B₁ ≥ 0 H₂: B₁< < 0 Ho: B₁ = 0 Ha: B₁ * 0 O Ho: B₁ * 0 Ha: B₁ = 0 о ново = 0 Ha: Bo # 0 Ho Bo # 0 Ha: Bo Find the value of the test statistic for the t-test. (Round your answer to three decimal places.) = = 0 Find the p-value. (Round your answer to four decimal places.) p-value What is your conclusion? O Reject Ho. We conclude that the relationship between years of experience and income is significant. O Do not reject Ho. We cannot conclude that the relationship between years of experience and income is significant. O Reject Ho. We cannot conclude that the relationship between years of experience and income is significant. O Do not reject Ho. We conclude that the relationship between years of experience and income is significant. (e) Calculate the coefficient of determination. (Round your…A medical researcher says that less than 76% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 500 adults in that country, 73% 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. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not nothing%. B. Less than 7676% of adults in the country think that healthy children should be required to be vaccinated. Your answer is correct. C. nothing% of adults in the country think that healthy children should be required to be vaccinated. D. More…
- A research center claims that 28% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 32% say that they would travel into space on a commercial flight if they could afford it. At a = 0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state Ho 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. At least % of adults in the country would travel into space on a commercial flight if they could afford it. B. No more than % of adults in the country would travel into space on a commercial flight if they.could afford it. C. 28 % of adults in the country would travel into space on a commercial flight if they could afford it. O D. The percentage adults in the country who would travel into…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…Suppose we obtain n observations from a sinusoid contaminated by Gaussian noise: X = A· sin(2 · T· f·k+¢) + Wk, k = 1, 2, ...,n, %3D where Wg are independent identically distributed (iid) Gaussian random variables with mean o and variance o?. The frequency f and phase o are known constants, while A is an unknown constant. Find the maximum likelihood estimator for A. Show all work.
- A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n=10n=10 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the df column.) S.S. d.f. M.S. F Between 6.68 Within 4.35 TOTAL Use the =FDIST() function in Excel to locate the p-value for this ANOVA:p-value = Report p-value accurate to at least 6 decimal places.If you use a significance level of α=.05α=.05, what would you conclude about these treatments?A medical researcher says that less than 86% 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, 84% think that healthy children should be required to be vaccinated. At α=0.05, 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 8686% 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 nothing%. C. nothing% of adults in the country think that healthy children should be required to be vaccinated. D. More than nothing%…This problem explores the question of estimating o(> 0) using a confidence interval based on a random sample X1, X2, ..., Xn from the distribution with pdf fo(x) = {& exp(- 20 if x > 0 otherwise. (a) Find the pdf of X2 by finding the cdf and differentiating it. (b) Using the result of (a) and techniques we developed in class, propose a pivot for estimating using a confidence interval and find the distribution of your pivot. Review Slides 38-41 of the power points for Chapter 7.1 to remind yourself how a pivot is used to construct a confidence interval. (c) Using the pivot obtained in (b) and the fact that o> 0, write down the formula for finding a short 100(1-a)% confidence interval for o. (d) Using the formula obtained in (c), compute the width of the resulting 95% confidence interval when n = 1 and ₁ = 1. (e) Is the 95% confidence interval for a you obtained in (d) when n = 1 and ₁ = 1 the shortest possible? If your answer is yes, explain why. If the answer is no, give a…