T Intervals for Means
Quiz
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
Anthony Clark
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20 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?
We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.
We are 95% confident that the interval (150, 350) captures the true average caloric content.
We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.
None of these are correct.
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.
89.08 < μ < 94.92
87.27 < μ < 96.73
87.29 < μ < 96.71
87.77 < μ < 96.23
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery. What is the Confidence Interval to one decimal place?
(114.5, 125.6)
(112.8, 127.4)
(112.82, 127.38)
(114.56, 125.64)
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...
The t distribution is more accurate than a z distribution.
Clarity ratings for the entire bacth are normally distributed.
The t-distribution will create a narrower interval than z.
The standard deviation for the population is unknown.
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Why do we use a t-distribution instead of a z-distribution for means?
Because the population standard deviation is UNKNOWN and it accounts for a greater variability present in SMALL samples.
It allows us to decrease the margin of error without increasing our confidence level.
It allows us to use the population standard deviation.
Because the population standard deviation is KNOWN and it accounts for a greater variability present in LARGE samples.
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select 10 Variety A and 10 Variety B tomato plants. Then the researchers divide in half each of 10 small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The 10 differences (Variety A - Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and unimodal with no outliers. Which of the following is the best reason to use a one-sample t interval for a mean difference rather than a two-sample t interval for a difference in means to analyze these data?
The number of plots is the same for Variety A and Variety B plants.
The response variable, yield of tomatoes, is quantitative.
This is an experiment with randomly assigned treatments.
Each plot is given both varieties of tomato plant.
The sample size is less than 30 for both treatments.
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
One reason for using a t distribution instead of the standard Normal distribution to find critical values when calculating a level C confidence interval for a population mean is that...
z can be used only for large samples.
z requires that you know the population standard deviation σ.
z requires that you can regard your data as an SRS from the population.
z requires that the sample size is less than 10% of the en population size.
a z critical value will lead to a wider interval than at critical value.
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