1. Diabetes tends to be more prevalent in urban populations, but why this is so is not fully understood. A recent study1 on mice was designed to investigate the link between diabetes and air pollution. The study involved mice, with randomly selected to have filtered air pumped into their cage while the other breathed particulate matter that simulated common air pollution. The response variable is the amount of insulin resistance each mouse had after weeks. Higher insulin resistance indicates a greater risk for developing diabetes. Data recreated from information in Sun et. al. (2009), "Ambient Air Pollution Exaggerates Adipose Inflammation and Insulin Resistance in a Mouse Model of Diet-Induced Obesity", Journal of the American Heart Association, 119 (4), 538-546. 1 (d) Using the information given in part (c), what is the Round your answer to one decimal place. p-value: _____ -value? 2. Null and alternative hypotheses for a test are given below. Give the notation ( , for example) for a sample statistic we might record for each simulated sample to create the randomization distribution. versus 3. Null and alternative hypotheses for a test are given below. Give the notation ( , for example) for a sample statistic we might record for each simulated sample to create the randomization distribution. versus 4. Null and alternative hypotheses for a test are given below. Give the notation ( , for example) for a sample statistic we might record for each simulated sample to create the randomization distribution. versus 5. We look at finger tapping rates to see if ingesting caffeine increases average tap rate. The sample data for the subjects ( randomly getting caffeine and with no caffeine) are given below. To create a randomization distribution for this test, we assume the null hypothesis is true, i.e. there is no difference in average tap rate between the caffeine and no caffeine groups. Create one randomization sample by randomly separating the data values into two groups. Find the sample mean of each group, and calculate the difference, , in the simulated sample means. The difference in the simulated sample means is= 6. (ex 129) A Randomization Distribution for 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 ppb, so we are testing vs , 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. A sample of chickens from one supplier is tested, and the resulting sample mean is . Subtracting mean down to the null mean of from the sample data to move the results in the following data: . (a) Use StatKey or other technology to create the randomization distribution for this test. Find the -value. -value (b) What is the conclusion of the test (using a 7. (ex 130) significance level)? Effect of Sleep and Caffeine on Memory A study is conducted in which a random sample of adults are divided equally into two groups and given a list of words to memorize. During a break, one group takes a minute nap while another group is given a caffeine pill. The response variable of interest is the number of words participants are able to recall following the break. We are testing to see if there is a difference in the average number of words a person can recall depending on whether the person slept or ingested caffeine. The data1 are shown in Table 1 below. sleep caffeine (a) State the null and alternative hypotheses. Let group and let group be the group where the words are recalled after sleep be the group where words are recalled after caffeine. (b) What statistic will we record for each of the simulated samples, to create the randomization distribution? C) Value of observed sample= d) where will randomization distribution be centered? e) Find one point on the randomization distribution by randomly dividing the data values into two groups. Compute the sample mean in each group, and compute the difference in the sample means for this simulated result. Round your answer to the nearest integer. The difference in sample mean is: f) Use StatKey or other technology to create a randomization distribution. Estimate the -value for the observed difference in means given in part (b) and part (c). Round your answer to two decimal places. P value is: 8) Exercise 131 Scientists studying lion attacks on humans in Tanzania1 found that lion attacks happened between pm and pm within either five days before a full moon or five days after a full moon. Of these, happened during the five days after the full moon while the other happened during the five days before the full moon. Does this sample of lion attacks provide evidence that attacks are more likely after a full moon? In other words, is there evidence that attacks are not equally split between the two five-day periods? (Note that this is a test for a single proportion since the data come from one sample.) (a) State the null and alternative hypotheses. (b) Use StatKey or other technology to find the Round your answer to three decimal places. -value. 9. exercise 132 After exercise, massage is often used to relieve pain, and a recent study1 shows that it also may relieve inflammation and help muscles heal. In the study, eleven male participants who had just strenuously exercised had minutes of massage on one quadricep and no treatment on the other, with treatment randomly assigned. After hours, muscle biopsies were taken and production of the inflammatory cytokine interleukinwas measured relative to the resting level. The differences (control minus massage) are given in Table 1 below (b) What is the sample mean difference in inflammation between no massage and massage? sample mean difference (d) Use StatKey or other technology to find the randomization distribution. Round your answer to three decimal places. -value= -value from a