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 two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis at the 5% level. Relaxed time (seconds) 29 48 28 22 23 45 37 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) Part (b) Part (c) Part (d) State the distribution to use for the test. (Enter your answer in the form z or far where df is the degrees of freedom.) Part (e) Jumping time (seconds) 20 43 29 21 25 43 35 32 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? O p-value < 0.010 O 0.010 < p-value < 0.050 O 0.050 < p-value < 0.100 O p-value > 0.100 Explain what the p-value means for this problem. O If Ho is true, then there is a chance equal to the p-value that the sample average difference between jumping times and relaxed times is between -1.625 and 1.625. O If Ho is false, then there is a chance equal to the p-value that the sample average difference between jumping times and relaxed times is -1.625 or less OR 1.625 or more. O If Ho 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 -1.625 and 1.625. O If Ho is true, then there is a chance equal to the p-value that the sample average difference between jumping times and relaxed times is -1.625 or less OR 1.625 or more.

In a fishing lodge brochure, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 71 out of a random sample of 86 guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use ? = 0.05.   (a) What is the level of significance?   State the null and alternate hypotheses. H0: p = 0.75; H1: p > 0.75H0: p ≠ 0.75; H1: p = 0.75    H0: p < 0.75; H1: p = 0.75H0: p = 0.75; H1: p ≠ 0.75H0: p = 0.75; H1: p < 0.75 (b) What sampling distribution will you use? The Student's t, since np > 5 and nq > 5.The standard normal, since np > 5 and nq > 5.    The Student's t, since np < 5 and nq < 5.The standard normal, since np < 5 and nq < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.)   (c) Find the P-value of the test…

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 two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis at the 5% level. Relaxed time (seconds) 29 48 28 22 23 45 37 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) Part (b) Part (c) + Part (d) Part (e) Part (f) Part (g) Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) απ (ii) Decision: O reject the null hypothesis Jumping time (seconds) 20 43 29 21 25 43 35 32 do not reject the…

X10.2.21-T Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 247 of 700 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the a=0.01 level of significance. Because npo (1- Po) = 172.5 > 10, the sample size is less than 5% of the population size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? versus H,: Ho: (Type integers or decimals. Do not round.)