List two unbiased estimators and their corresponding parameters. (Select all that apply.) μ is an unbiased estimator for x p̂ is an unbiased estimator for p p is an unbiased estimator for p̂ x is an unbiased estimator for μ σx is an unbiased estimator for σ σ is an unbiased estimator for σx
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List two unbiased estimators and their corresponding parameters. (Select all that apply.)
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- List two unbiased estimators and their corresponding parameters. (Select all that apply.) p is an unbiased estimator for p̂σ is an unbiased estimator for σxp̂ is an unbiased estimator for px is an unbiased estimator for μσx is an unbiased estimator for σμ is an unbiased estimator for xFor each of the following situations, identify whether the appropriate test is a paired t-test (for parameter µd) or a two-sample t-test (for parameter µ1 - µ2). Briefly explain your answer. Sixty students were matched by initial pulse rate, with the two with the highest pulse forming a pair, and so on. Within each pair, one student was randomly chosen to drink a caffeinated beverage, while the other one drank an equivalent amount of water. Their pulse rates were measured 10 minutes later, to test whether caffeine consumption elevates pulse rates. To determine whether lack of sleep increases appetite, researchers recruited 50 volunteers and randomly assigned 25 of them to sleep at least 8 hours a night and the other 25 to sleep at most 5 hours a night, for 3 days. Calorie intake was recorded for all 50 volunteers for the 3-day period.As a bonus assignment a former student checked if your professor gave a statisticallysignificant difference in grades between his male and female students. She based herstudy based on grades assigned in intermediate Econ courses (Econ 303, 305 and 317)and her sample included nm = 485 male students and nf = 264 female students. Theaverage grades received were xm = 84.6 and xf = 85.8 The population standad deviation were σ m = 12.0 and σ f = 11.4 8. From the same extra-credit study as in question 7 see above, this former student found that the proportion of female students in principle courses (Econ 203, 205) was ?̅? = 0.380, while the proportion of female students in intermediate courses (Econ 303, 305, 317) was ?̅? = 0.352. The principle courses sample size was np = 782, while the intermediate courses sample size was ni = 749. Test the hypothesis that female students are less in intermediate courses using a 90% confidence level and the p-value approach.
- Claim: A majority of adults would erase all of their personal information online if they could. A software firm survey of 653 randomly selected adults showed that 61% of them would erase all of their personal information online if they could. Complete parts (a) and (b) below. a. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information. ▼ sigmaσ muμ pp ▼ greater than> less than< not equals≠ equals= enter your response hereFor each of the following settings, define the parameter of interest and write the appropriate null and alternative hypotheses for the test that is described. Scenario 1: In an avocado, the average seed diameter is 1 inch. However, you are an avocado expert and you believe that the average seed diameter is increasing recently.Give at least one reason why the following statements are incorrect.a) If X ~ Bi(4, p), P(X<=2) = P(X>=2) for any pb) If X ~ Po(5), then P(X > 3) = P(X = 4) + P(X = 5). c) If X is continuous quantitative,then P(X<=1) = P(X = 0) + P(X = 1). d) If 2 X ~ N(population mean , (population standard deviation)^2) and a > 0, then P( a<=X-population standard deviation<=2a) = 2P(Z<=a/population standard deviation) -1.e) chi-squared of (k) is symmetrical with respect to k.
- Which of the following is NOT CORRECT? A) The past purchase frequency (freqi) affects the purchase probability positively – i.e., customers with high past purchase frequency are more likely to purchase our product in the next year than those with low past purchase frequency. B) In general, customers are likely to buy our product because the baseline parameter is negative. C) High-income customers are more likely to purchase our product in the next year than low- income customers because the coefficient corresponding to the income variable (incomei) is positive. D) Although the number of flyers (nmaili) positively affects the purchase probability, it is not guaranteed that sending flyers to customers as many as possible maximizes profits.A scientist studying local lakes claims that there is a linear relationship between a lake’s level of mercury and the lake’s depth. The scientist collected data to test the claim at a significance level of α=0.01. The following hypotheses were tested. H0:β1=0Ha:β1≠0 The test yielded a t-value of 2.7 and a p-value of 0.012. Which of the following is a correct conclusion about the scientist’s claim? The null hypothesis is rejected since 0.012>0.01. There is sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth. A The null hypothesis is not rejected since 0.012>0.01. There is sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth. B The null hypothesis is rejected since 0.012>0.01. There is not sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth.…Produce a CROSSTAB for the variables DEGREE and MARHOMO. Before conducting the analyses, reverse code MARHOMO into R_MARHOMO so that 1 = Strongly Disagree; 2 = Disagree; 3 = Neither Agree nor Disagree; 4 = Agree; and 5 = Strongly Agree. Then, examine the relationship between these variables by testing both statistical significance and strength of association. Use chi-square for significance and choose the appropriate measures for strength of association (Phi, Cramer’s V, Lambda, or Gamma). Set alpha to .05. State the null and research hypotheses: H0: H1: What is the obtained chi-square value? What is the significance level (p-value) for the obtained chi-square? Should we reject or fail to reject the null hypothesis? Is there a statistically significant relationship between these variables? Which measure of association would be most appropriate for these variables? What is the value of the measure of association? Interpret your findings by explaining in full sentences whether there is a…
- To increase egg production, a farmer decided to increase the number of times the lights in his henhouse were on. Ten hens were randomly selected, and the number of eggs each produced was recorded. After one week of lengthened light time, the same hens were monitored again. The data is given here. At α = 0.05, can it be concluded that the increased light time increased egg production? Hen 1 2 3 4 5 6 7 8 9 10 Before 4 3 8 7 6 4 9 7 6 5 After 6 5 9 7 4 5 10 6 9 6Which one is correct? Consider the Cobb- Douglas production function, Q = aK^bL^c ; b and ca) Can be estimated using OLS on the equation Q = a +bK+cL b) Can be calculated from the covariances of K and L with Qc) cannot be estimated using OLS d) can be estimated using OLS on the equation log(Q) =log(a) +b log(K) +b log(L)A researcher collects data that represents the average number of hours of sleep in the last two nights by 8 depressed patients and 9 non-depressed patients. The researcher is interested in whether the two groups reliably differ in the amount of sleep they get. Use Jamovi to calculate t-obt and the p value.
