A student wants to determine the proportion of times a spun penny will land on heads. She spins a penny 50 times and records the number of times it lands on heads. What type of sampling is described in this study?
A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students that are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75,0.75,0.75,0.5,1,1.25 She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. The student plans to test the hypotheses, ratio of cap h sub 0 to mu is equal to 1 versus ratio of cap h sub A to mu is less than 1 , where mu is equal to the true mean amount of time that statistics students spend doing statistics homework each night. Are the conditions for inference met?
A drug manufacturing company believes it has found a new medication to alleviate pain for headache sufferers. Twenty people with chronic headaches are asked to take a placebo pill or a pill containing the new medication during their next headache episode. The pill they take is determined by a coin flip. An hour later, the participants are asked to rate their headache pain level on a scale from 1 (no pain) to 5 (severe pain). During their next headache episode, the subjects are asked to take the other pill. The difference in pain ratings open paren new pill minus placebo close paren is calculated for each subject. Are the conditions for inference met?
The daily temperatures in fall and winter months in Virginia have a mean of 62 times degree F A meteorologist in southwest Virginia believes the mean temperature is colder in this area. The meteorologist takes a random sample of 15 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 58 times degree F with a standard deviation of 4 point 1 2 times degree F A significance test at an alpha level of α=0.05 produces a cap p -value of 0 point 0 0 1 What is the correct interpretation of the cap p -value?
The amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. A student claims that the average travel time to school for his large district is 20 minutes. To further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22 point 4 minutes with a standard deviation of 5 point 9 minutes. He would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. What are the appropriate hypotheses?
A study was conducted to determine the true mean number of hours of television watched on school nights by teenagers. A 99 percent confidence interval for the true mean is 0 point 8 hours to 2 point 1 hours. Based upon this interval, what conclusion should be made about the hypotheses: ratio of cap h sub 0 to mu is equal to 2 point 5 versus ratio of cap h sub A to mu is not equal to 2 point 5 where μ= the true mean number of hours of television watched on school nights by teenagers at α=0.01 ?
A company that sells hair-care products wants to estimate the mean difference in satisfaction rating for a product that combines shampoo and conditioner compared with a shampoo and conditioner used separately. A researcher recruits 60 volunteers and pairs them according to age, hair color, and hair type. For each pair, the researcher flips a coin to determine which volunteer will use the shampoo/conditioner combination and which one will use the separate shampoo and conditioner. After using the products for one month, the subjects will be asked to rate their satisfaction with the hair products on a scale of 1 – 10 ( 1 is equal to highly dissatisfied and 10 is equal to highly satisfied). The mean difference in satisfaction ratings open paren Combined minus Separate close paren is calculated. What is the appropriate procedure?
The daily temperatures in fall and winter months in Virginia have a mean of 62 times degree F A meteorologist in southwest Virginia believes the mean temperature is colder in this area. The meteorologist takes a random sample of 30 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 59 times degree F with a standard deviation of 6 point 2 1 times degree F Do the data provide convincing evidence at the alpha is equal to 0 point 0 5 level that the mean temperature in fall and winter months in southwest Virginia is less than 62 times degree F ? What hypotheses should the meteorologist use to conduct a significance test?
The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than the volunteers without training. The researcher tests ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is greater than 0 , where mu sub 1 is equal to the true mean amount of time that volunteers who were given training held their breath and mu sub 2 is equal to the true mean amount of time that volunteers without training held their breath. The conditions for inference are met. What is the value of the test statistic for a t -test about a difference in means?
Assuming the conditions for inference are met, what is the cap p -value for testing the hypotheses ratio of cap h sub 0 to mu sub diff is equal to 0 ; ratio of cap h sub A to mu sub diff is greater than 0 ? Use the t -table.
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