AnswersStatisticsTesting Claims about Means

Practice Test Answers

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6

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?

A
There is a 0 point 1 percent probability that a sample mean temperature of 58 times degree F will occur by chance alone if the true mean temperature is 62 times degree F .
B
Assuming the true mean temperature is 62 times degree F , there is a 99 point 9 percent probability that a sample mean of 58 times degree F will occur by chance alone.
C
Assuming the true mean temperature is 62 times degree F , there is a 0 point 1 percent probability that the null hypothesis is true by chance alone.
D
There is a 0 point 1 percent chance that a sample mean temperature of at most 58 times degree F will occur by chance if the true mean temperature is 62 times degree F .
7

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
ratio of cap h sub 0 to mu is equal to 20 versus ratio of cap h sub A to mu is less than 20 , where mu is equal to the mean travel time for the 50 students who were part of this study
B
ratio of cap h sub 0 to mu is equal to 20 versus ratio of cap h sub A to mu is less than 20 , where mu is equal to the true mean travel time for all students who attend this school
C
ratio of cap h sub 0 to mu is equal to 20 versus ratio of cap h sub A to mu is greater than 20 , where mu is equal to the true mean travel time for all students who attend this school
D
ratio of cap h sub 0 to mu is equal to 20 versus ratio of cap h sub A to mu is greater than 20 , where mu is equal to the mean travel time for the 50 students who were part of this study
8

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
Fail to reject cap h sub 0 . Since 2 point 5 falls outside the 99 percent confidence interval, there is convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2 point 5 hours.
B
Reject cap h sub 0 . Since 2 point 5 falls outside the 99 percent confidence interval, there is not convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2 point 5 hours.
C
Reject cap h sub 0 . Since 2 point 5 falls outside the 99 percent confidence interval, there is convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2 point 5 hours.
D
Fail to reject cap h sub 0 . Since 2 point 5 falls outside the 99 percent confidence interval, there is not convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2 point 5 hours.
10

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?

A
ratio of cap h sub 0 to line segment x is less than 62 times degree F ; ratio of cap h sub alpha to line segment x is equal to 62 times degree F
B
ratio of cap h sub 0 to mu is equal to 62 times degree F ; ratio of cap h sub alpha to mu is less than 62 times degree F
C
ratio of cap h sub 0 to mu is equal to 62 times degree F ; ratio of cap h sub alpha to mu is greater than 62 times degree F
D
ratio of cap h sub 0 to line segment x is equal to 62 times degree F ; ratio of cap h sub alpha to line segment x is less than 62 times degree F
11

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?

A
t is equal to the fraction with numerator 89 point 6 7 minus 48 point 3 3 and denominator square root of the fraction with numerator 15 point 8 3 squared and denominator 6 plus the fraction with numerator 9 point 8 1 squared and denominator 6 end root
B
t is equal to the fraction with numerator 89 point 6 7 minus 48 point 3 3 and denominator square root of the fraction with numerator 15 point 8 3 squared and denominator 5 plus the fraction with numerator 9 point 8 1 squared and denominator 5 end root
C
t is equal to the fraction with numerator 89 point 6 7 minus 48 point 3 3 and denominator square root of the fraction with numerator 15 point 8 3 times open paren 1 minus 15 point 8 3 close paren and denominator 5 plus the fraction with numerator 9 point 8 1 times open paren 1 minus 9 point 8 1 close paren and denominator 5 end root
D
t is equal to the fraction with numerator 89 point 6 7 minus 48 point 3 3 and denominator square root of the fraction with numerator 15 point 8 3 times open paren 1 minus 15 point 8 3 close paren and denominator 6 plus the fraction with numerator 9 point 8 1 times open paren 1 minus 9 point 8 1 close paren and denominator 6 end root

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