Statistic and Probability

Read each question carefully and follow all instructions exactly. Correct answers without adequate supporting work will not receive full credit, so show work whenever possible. It is likely that you will do some work using commands on your graphing calculator. When you do, write a brief description of what you did like “data in L1, 1-Var Stat”.
Put all work and answers in the indicated spaces on the answer sheet provided. Be sure your final answer is clear (boxed or circled). When graphing USE A RULER! Unless the problem gives specific rounding instructions, use the general rules found in the Rounding Rules document.
For all Hypothesis Test Questions you must:
State both the null & alternative hypotheses
State which test or test statistic you are using
State the p-value (or critical value if using the classical approach)
State your conclusion (i.e. “This is sufficient evidence to support the claim that students who take notes perform better on the test.”)
The following figures represent amounts of time (in seconds) a random sample of students from this class spent watching the videos for chapter 8. At = 0.01, us this data to test the claim that the average time spent was less than the total run time of the videos (total run time = 435 seconds)

608 610 408 404 516 500
9 947 624 2 514 495
940 501 251 536 700 435
28 0 713 233 4 5
540 511 188 352 486 201

Last year the Chronicle reported that average rent for a one-bedroom apartment in Center City was $1229. Lucas just moved to town. He looked at 17 one-bedroom apartments and their average rent was $1350 with a standard deviation of $175. Treat Lucas’ apartment search as a simple random sample, assume that rents are normally distributed and test if rent for a one-bedroom apartment has gone up since last year at the =0.05 level of significance.

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A website states that 10% of adults in the US believe they have experienced an encounter with an alien. Velma believes this statement is an exaggeration (surely, less than 10% of adults believe they have met an alien, she thinks). For her Statistics project Velma surveys 400 adults and finds that 31 of them believe they have experienced an alien encounter. Use this data to test Velma’s claim at the = 0.1 level of significance.

Information published by a large fast-food chain indicates that the standard deviation in wait times at their drive-thrus nationwide is 2.5 minutes (or less). You feel like your wait time varies more widely so you take simple random sample of 40 drive-thru visits and find the standard deviation in your sample to be 2.7 minutes. At the = 0.05 level of significance, does this data support your feeling? [Assume that wait times are normally distributed.]

At a large urban hospital high school students and senior citizens are the primary volunteers. The table below summarizes a simple random sample of recent volunteer hours for each group. Does the data indicate a difference in the average number of hours worked for the two different groups at the = 0.05 level of significance?
High schoolers Senior Citizens
n_1 =40 n_2 = 59
x ̅_1 =344 x ̅_2 = 722
s_1 = 3.6 s_2 = 4.2

The data below shows the time (in seconds) that took 9 randomly selected individuals to complete a 16-piece, child’s puzzle both while sober and while legally intoxicated. Does this data indicated a statistically significant slowing of puzzle-solving abilities while intoxicated at the = 0.10 level of significance? [Assume the data come from a normally distributed population with no outliers.]
Sober 45 56 67 46 54 70 52 62 73
Intoxicated 69 75 100 105 78 101 82 75 96
A researcher wonders about the daily health habits of doctors versus other professionals of similar education. As part of her research, she randomly surveys 100 doctors and 115 other professionals and asks they if they take any daily health supplements (vitamins, herbal supplements, etc.). 36 of the doctors and 45 of the other professionals report taking at least one daily supplement. Does this data support the claim that the behavior of doctors is different than that of other professionals at the = 0.10 level of significance?