Q1

\fIn words, smte what your random variable )7},be Xmmhybn-d represents. 0 )7\"be Ynomhybm. represents the dierence in the miles per gallon of non-hybrid and hybrid sedans. O )7\"be 10},be represents the average d'rlference in the miles per gallon of non-hybrid and hybrid sedans. O )7"be 10\El Part [n What is the pvalue? (Round your answer to four decimal places.) :| Explain what the Name means for this problem, 0 If H0 is false: then there is a chance equal to the pvalue that the sample average gas mileage of non-hybrid sedans is 12 mpg more than the sample average gas mileage of hybrid sedans. 0 If H0 is true, then there is a chance equal to the pvalue that the sample average gas mileage of nonhybrid sedans is at least 12 mpg less than the sample average gas mileage of hybrid sedans 0 If H0 is false: then there is a chance equal to the pivalue that the sample average gas mileage of nonihybrid sedans is at least 12 mpg less than the sample average gas mileage of hybrid sedans. 0 If H0 is true, then there is a chance equal to the pvalue that the sample average gas mileage of nonehybrid sedans is 12 mpg more than the sample average gas mileage of hybrid sedans. El Part [9) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the pivalue. pvalu ihybrid 7 incurhybrid u lot xhybrid - Xmm-hybrtd xhybrid - Xmm-hybrtd El Part [h] Indicate the correct decision ('\"reject\" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (ijAlpha (Enter an exact number as an integer, fraction, or decimal.) (ii) Decision: 0 reject the null hypothesis 0 do not reject the null hypothesis (iii) Reason for decision: 0 Since p-value :> a, we do not reject the null hypothesis. 0 Since pvalue a, we reject the null hypothesis. 0 Since pvalue a, we reject the null hypothesis. 0 Since prvalue or, we do not reject the null hypothesis. (iv) Conclusion: 0 There is sufcient evidence to show that the mean entry level mechanical engineering salary is lower than the mean entry level electrical engineering salary 0 There is not sufcient evidence to show that the mean entry level mechanical engineering salary is lower than the mean entry level electrical engineering salary. El Part [i] Explain how you determined which distribution to use 0 The tdistribution will be used because the samples are independent and the population standard deviation is not known. 0 The standard normal distribution will be used because the samples are independent and the population standard dewation is known 0 The standard normal distribution will be used because the samples involve the difference in proportions. O The tdistribution will be used because the samples are dependent El Part{b} State the alternative hypothesis. 0 Ha: pd = O 0 Ha: ,ud 0 El Part {1:} In words, state what your random variable Yd represents. 0 Rd represents the difference in time for each girl to hold her breath while relaxed and while jumping. 0 Rd represents the difference in the average amount oftime a girl can hold her breath while relaxed and while jumping. 0 Rd represents the amount of time each girl can hold her breath. 0 Rd represents the average difference in the length of time each girl can hold her breath. El Part {(1} State the distribution to use for the test. (Enter your answer in the form 2 or tdfwhere df is the degrees of freedom.) El Part is} What is the test statistic? (If using the 2 distribution round your answer to two decimal places, and if using the tdistribution round your answer to three decimal places.) =: El Part") What is the p-value? O pvalue 0.100 Explain what the pvalue means for this problem. 0 If H0 is false, then there is a chance equal to the p-value that the sample average difference between jumping times and relaxed times is between 1.25 and 1.25. 0 If H0 is false, then there is a chance equal to the p-value that the sample average difference between jumping times and relaxed times is 1.25 or less OR 1.25 or more. 0 If H0 is true, then there is a chance equal to the pvalue that the sample average difference between jumping times and relaxed times is between 1.25 and 1.25. 0 If H0 is true, then there is a chance equal to the pvalue that the sample average difference between jumping times and relaxed times is 1.25 or less OR 1.25 or more. At Rachel's 11th birthday party, 8 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a twominute rest, they timed themselves while jumping. The girls thought that the mean difference between theirjumping and relaxed times would be zero. Test their hypothesis at the 5% level. Relaxed time (seconds) Jumping time (seconds) 27 20 45 41 28 29 22 21 23 25 45 43 37 35 29 32 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) El Part [a] State the null hypothesis