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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1If X1, X2, ... , Xn constitute a random sample of size nfrom a geometric population, show that Y = X1 + X2 +···+ Xn is a sufficient estimator of the parameter θ.A study found that 1 out of 200 adult males have green eyes. If a random sample of 400 adult males is obtained, is the sampling of the sample proportion of males that have green eyes approximately normal? A. Yes, the sample size is greater than 10% of the population. B. Yes, the sample was randomly selected C. No, because np < 10 D. No, because nq < 10
- A random sample of n1=17�1=17 securities in Economy A produced mean returns of x̄ 1=5.6% x̄ 1=5.6% with s1=2.3%�1=2.3% while another random sample of n2=20�2=20 securities in Economy B produced mean returns of x̄ 2=4.6% x̄ 2=4.6% with s2=2.3%.�2=2.3%. At α =0.2 α =0.2, can we infer that the returns differ significantly between the two economies? Assume that the samples are independent and randomly selected from normal populations with equal population variances ( σ 12= σ 22)( σ 12= σ 22). T-Distribution Table a. Calculate the test statistic. t=�= Round to three decimal places if necessary b. Determine the critical value(s) for the hypothesis test. + Round to three decimal places if necessary c. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to RejectThere are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 p(x1) 0.1 0.2 0.7 ? = 1.6, ?2 = 0.44 (a) Determine the pmf of To = X1 + X2. to 0 1 2 3 4 p(to) (b) Calculate ?To. ?To = How does it relate to ?, the population mean? ?To = · ? (c) Calculate ?To2. ?To2 = How does it relate to ?2, the population variance? ?To2 = · ?2If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y =X1 + 2X2 + X3 is not a sufficient estimator of θ. (Hint:Consider special values of X1, X2, and X3.)
- For a population with u=60 and o=4, the X value corresponding to z=1 would beThere are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). Can you help me with 3 and 4?Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose that the variable for consumption is measured with error, so conss = cons + e, where conss is the mismeaured variable, cons is the true variable, e is random, i.e., e is independent of all the regressors. What would we expect and why? A) OLS estimators for the coefficients will all be biased B) OLS estimators for the coefficients will all be unbiased C) ALL the standard errors will be bigger than they would be without the measurement error D) both B and C
- A sample of n=10observations is drawn from a normal population with μ=900 and σ=220. Find each of the following: A. P(X¯>1039) B. P(X¯<788) C. P(X¯>844)Q2. The samples ?⃗ 1 = (X11, X12, … , X1n ) and ?⃗ 2 = (X21,X22, … , X2n ) are drawn from a Normally distributed two populations with parameters (?1, ?1 ^2 ) and (?2, ?2^2 ), respectively. ?̅ 1 = 15.2, ?̅ 2 = 8.7, ?̂1? 2 = 25.8, ?̂2? 2 = 17.3, ?1 = 13, ?2 = 15 and ?1 ^2 = ?2 ^2 is known. Then, find confidence interval for the difference of the population means (?1 − ?2 ) at 90% confidence level.suppose that the proportions of blood phenotypes in a particular population are as follows a=0.40 b=0.12 ab=0.04 o=0.44 assume the phenotype of three randomly selected individuals are independent of one another. what is the probabililty that the phenotypes of three randomly selected individuals match?
