Consider the accompanying data on flexxural strength (MPa) for concrete beams of a certain type. 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.8 8.7 7.8 9.7 7.4 7.7 9.7 8.1 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.7 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.S 7.9 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.7 Prior to obtaining data, denote the beam strengths by X. X and the cylinder strengths by Y.. Y. Suppose that the X's constitute a random sample from a distribution with mean , and standard deviation a, and that the Y's form a random sample (independent of the X's) from another distribution with mean y and standard deviation o. Use rules of expected value to show that - is an unbiased estimator of , - H O EX - = E - EŨ O EX -) - VEX) - EY) = H; - H2 O EX - - E) - E -, - O EX -) - (E) - E) = H - Ha O EX - = nm(e) - EC) = #s - H Calculate the estimate for the given data. (Round your answer to three decimal places.) MPa I Use rules of variance to obtain vũ - - vũ - v expression for the variance and standard deviation (standard error) of the estimator in part (a). -= VX- Y) Compute the estimated standard error. (Round your answer to three decimal places.) MPa Calculate a point estimate of the ratio ale, of the two standard deviations. (Round your answer to three decimal places.) I Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate of the variance of the difference X - Y between beam strength and cylinder strength. (Round your answer to two decimal places.) MPa

Which of the following best describes the relationship between the variables on the scatter plot below? 11 10 15 4 3. 2 1 1234 56 7 8 9 10 11 12 13 O A. linear association OB. no association OC. non-linear association OD. linear and non-linear association

A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts (a) and (b) below. 191 175 173 191 190 175 181 165 184 193 185 Height (cm) of President Height (cm) of Main Opponent 178 C... Since the P-value is greater than the significance level, fail to reject the null hypothesis. There is not sufficient evidence to support the claim that presidents tend to be taller than their opponents. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is cm<< cm. (Round to one decimal place as needed.) What feature of the confidence interval leads to the same conclusion reached in part (a)? Since the confidence interval contains zero fail to reiect the null…

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