At Rachel's 11th birthday party, 8 girls were timed t see how long (in seconds) they could hold their breath in elves while jumping. The girls thought that laxed times would be zero . Test their hypothesis at the 5% level. Relaxed time (seconds) Jumping time (seconds) 19 48 29 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.) Part (a) State the null hypothesis. O Ho Ho =0 O HO : Ho = 0 O HO : H o 20 Part (b) State the alternative hypothesis. O He: Ma = 0 O Ha: Ma = 0 O Ha Ha # 0 Part (c) In words, state what your random variable Xo represents. OX. represents the difference in the average amour e average amount of time a girl can hold her breath while relaxed and while jumping. O Xy represents the amount of time each gi O Xy represents the difference in time for each girl to hold her breath while relaxed and while jumping. O Xy represents the average difference in the length of time each girl can hold her breath. Part (d) State the distribution to use for the test. (Enter your answer in the form z or tay Where of is the degrees of freedom.) Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) -Select--- = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem . O If Ho is false, then there is a chance equal to the p-value that the sample av times and relaxed times is between -2.125 and 2.125. O If Ho is false, then there is a chance equal to the p-V ed times is -2. 125 or less OR 2. 125 or more. O If Ho is true, then there is a chance equal to the p-value that the sample ave mping times and relaxed times is -2.125 or less OR 2.125 or more. O If Ho is true, then there is a cha es and relaxed times is between -2.125 and 2. 125. Part (9) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. p-value 1/2 (p-value 1/2(p-value: - Xd /2(p-value 1/2(p-value: P-value - Xd Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (1) Alpha (Enter an exact number as an integer, fraction, or decimal.) a = (ii) Decision: O reject the null hypothesis O do not reject the null hypothesis (ii) Reason for decision: O Since p-value > a, we do not reject the null hypothesis. Since p-value a, we reject the null hypothesis. O Since p-value