(a) The evidence against the null hypothesis is significant, but only at the 10% level.

Sleep or Caffeine for Memory? The consumption of caffeine to benefit alertness is a common activity practiced by 90% of adults in North America. Often caffeine is used in order to replace the need for sleep. One recent study1 compares students' ability to recall memorized information after either the consumption of caffeine or a brief sleep. A random sample of 35 adults (between the ages of 18-39 ) were randomly divided into three groups and verbally given a list of 24 words to memorize. During a break, one of the groups takes a nap for an hour and a half, another group is kept awake and then given a caffeine pill an hour prior to testing, and the third group is given a placebo. The response variable of interest is the number of words participants are able to recall following the break. The summary statistics for the three groups are in the table below. We are interested in testing whether there is evidence of a difference in average recall ability between any two of the treatments. Thus we have three possible tests between different pairs of groups: Sleep vs Caffeine, Sleep vs Placebo, and Caffeine vs Placebo.

1 Mednick, Cai, Kanady, and Drummond, "Comparing the benefits of caffeine, naps and placebo on verbal, motor and perceptual memory", Behavioural Brain Research, 193 (2008), 79-86.

Warning

Ok

Cancel

(a) In the test comparing the sleep group to the caffeine group, the p-value is 0.003. What is the conclusion of the test? H0. In the sample , which group had better recall ability? According to the test results, do you think sleep is really better than caffeine for recall ability?

Warning

Ok

Cancel

(b) In the test comparing the sleep group to the placebo group, the p-value is 0.06. What is the conclusion of the test, using a 5% significance level? H0. What is the conclusion of the test, if we use a 10% significance level? H0. How strong is the evidence of a difference in mean recall ability between these two treatments?

Warning

Ok

Cancel

(c) In the test comparing the caffeine group to the placebo group, the p-value is 0.22. What is the conclusion of the test? H0. In the sample , which group had better recall ability? According to the test results, would we be justified in concluding that caffeine impairs recall ability?

Warning

Ok

Cancel

Take a nap.

Have a placebo.

Have some coffee.

Don't show me this message again for the assignment

Chapter 4, Section 4, Exercise 128

Arsenic in Chicken A restaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb, so we are testing H0: =80 vs Ha: >80, where represents the average level of arsenic in all chicken from a certain supplier. It takes money and time to test for arsenic so samples are often small. Suppose n=6 chickens from one supplier are tested, and the level of arsenic (in ppb) are

63,71,82,92,93,139.

Warning

Ok

Cancel

(a) What is the sample mean for the data? Round your answer to the nearest integer. x=

Warning

Ok

Cancel

the tolerance is +/-2%

(b) Translate the original sample data by the appropriate amount to create a new data set in which the null hypothesis is true. How do the sample size and standard deviation of this new data set compare to the sample size and standard deviation of the original data set?

Warning

Ok

Cancel

(c) Write the six new data values from part (b) on six cards. Sample from these cards with replacement to generate one randomization sample. (Select a card at random, record the value, put it back, select another at random, until you have a sample size of 6 , to match the original sample size.) Give the sample mean. x=

Warning

Ok

Cancel

the tolerance is +/-2%

Chapter 5, Section 1, Exercise 013

Find the specified areas for a normal density.

Warning

Ok

Cancel

(a) The area below 77 on a N(75,10) distribution Round your answer to three decimal places. area=

Warning

Ok

Cancel

the tolerance is +/-2%

(b) The area above 26 on a N(20,6) distribution Round your answer to three decimal places. area

Warning

Ok

Cancel

the tolerance is +/-2%

Don't show me this message again for the assignment

Chapter 5, Section 1, Exercise 020

Find endpoint(s) on the given normal density curve with the given property.

Warning

Ok

Cancel

(a) The area to the left of the endpoint on a N(5,4) curve is about 0.10. Round your answer to two decimal places. endpoint

Warning

Ok

Cancel

the tolerance is +/-2%

Don't show me this message again for the assignment

Chapter 5, Section 1, Exercise 028

Warning

Ok

Cancel

Choose the graph for the middle 80% for a standard normal distribution.

Warning

Ok

Cancel

Choose the graph for the the middle 80% for a standard normal distribution converted to a N(100,15) distribution.

Chapter 5, Section 1, Exercise 040

Curving Grades on an Exam A statistics instructor designed an exam so that the grades would be roughly normally distributed with mean =75 and standard deviation δ=11. Unfortunately, a fire alarm with ten minutes to go in the exam made it difficult for some students to finish. When the instructor graded the exams, he found they were roughly normally distributed, but the mean grade was 60 and the standard deviation was 18. To be fair, he decides to ‘‘curve” the scores to match the desired N(75,11) distribution. To do this, he standardizes the actual scores to z-scores using the N(60,18) distribution and then ‘‘unstandardizes” those z-scores to shift to N(75,11). What is the new grade assigned for a student whose original score was 45? Round your answer to the nearest integer. new score= How about a student who originally scores an 87? Round your answer to the nearest integer. new score

Don't show me this message again for the assignment

Chapter 5, Section 2, Exercise 061

Smoke-Free Legislation and Asthma Hospital admissions for asthma in children younger than 15 years was studied1 in Scotland both before and after comprehensive smoke-free legislation was passed in March 2006. Monthly records were kept of the annualized percent change in asthma admissions, both before and after the legislation was passed. For the sample studied, before the legislation, admissions for asthma were increasing at a mean rate of 5.2% per year. The standard error for this estimate is 0.7% per year. After the legislation, admissions were decreasing at a mean rate of 18.2% per year, with a standard error for this mean of 1.79%. In both cases, the sample size is large enough to use a normal distribution. 1Mackay, D., et. al., ‘‘Smoke-free Legislation and Hospitalizations for Childhood Asthma,” The New England Journal of Medicine, September 16, 2010; 363(12):1139-45.

Warning

Ok

Cancel

(a) Find a 95% confidence interval for the mean annual percent rate of change in childhood asthma hospital admissions in Scotland before the smoke-free legislation. Round your answers to one decimal place. The 95% confidence interval is to .

Warning

Ok

Cancel

(b) Find a 95% confidence interval for the same quantity after the legislation. Round your answers to one decimal place. The 95% confidence interval is to .

Warning

Ok

Cancel

(c) Is this an experiment or an observational study?

Warning

Ok

Cancel

(d) The evidence is quite compelling. Can we conclude cause and effect?

Chapter 5, Section 2, Exercise 064

Penalty Shots in World Cup Soccer A study1 of 138 penalty shots in World Cup Finals games between 1982 and 1994 found that the goalkeeper correctly guessed the direction of the kick only 41% of the time. The article notes that this is ‘‘slightly worse than random chance.” We use these data as a sample of all World Cup penalty shots ever. Test at a 5% significance level to see whether there is evidence that the percent guessed correctly is less than 50%. The sample size is large enough to use the normal distribution. The standard error from a randomization distribution under the null hypothesis is SE=0.043. 1St.John, A., ‘‘Physics of a World Cup Penalty-Kick Shootout - 2010 World Cup Penalty Kicks,” Popular Mechanics, June 14, 2010.

Warning

Ok

Cancel

State the null and alternative hypotheses.

What is the test statistic? Round your answer to two decimal places. z=

Warning

Ok

Cancel

the tolerance is +/-2%

What is the p-value? Round your answer to three decimal places. p-value=

Warning

Ok

Cancel

the tolerance is +/-2%

What is the conclusion?

Chapter 5, Section 2, Exercise 065

How Often Do You Use Cash? In a survey1 of 1000 American adults conducted in April 2012, 43% reported having gone through an entire week without paying for anything in cash. Test to see if this sample provides evidence that the proportion of all American adults going a week without paying cash is greater than 40%. Use the fact that a randomization distribution is approximately normally distributed with a standard error of SE=0.016. Show all details of the test and use a 5% significance level. 1‘‘43% Have Gone Through a Week Without Paying Cash,” Rasmussen Reports, April 11, 2011.

Warning

Ok

Cancel

State the null and alternative hypotheses.

What is the test statistic? Round your answer to two decimal places. z=

Warning

Ok

Cancel

the tolerance is +/-2%

What is the p-value? Round your answer to two decimal places. p-value=

Warning

Ok

Cancel

the tolerance is +/-2%

What is the conclusion?

Warning

Ok

Cancel