Suppose n = 41 and p = 0.37. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np =  nq = What are the values of ?p̂ and ?p̂? (Use 3 decimal places.)

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…

Each of the boxplots shown summarizes 24 student scores on a recent test in two different classes. The boxplots are drawn using a common numerical scale. Which of the following must be true?    1. The lower 25% of Class B are much more spread out than the lower 25% of Class A 2. More people scored below the lower quartile for Class A than Class B 3. The distribution for Class B is skewed left and has a noticeable outlier as well, while the distribution for Class A is somewhat skewed right 4.Class A had more people between the median and the lower quartile than Class B. 3.The distribution for Class A is somewhat symmetric, while the distribution for Class B is skewed right with a noticeable outlier as well

3a) The mean IQ of 200 patients in a psychiatric hospital is 91, with a variance of 16, and the distribution is highly negatively skewed. Between what two IQ scores would we expect to find at least 160 of the patients falling? b) If the distribution was mound-shaped and symmetrical, with the same mean and standard deviation as in part A, approximately how many patients would have IQ scores at or below the 5th percentile or above a score of 97? Answers: a) 82 to 100 b) 28.5 or 29